LMFDB - Embedded newform 966.2.q.i.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.2
Character	$\chi$	$=$	966.463
Dual form			966.2.q.i.169.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.987362 + 1.13948i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.987362 + 1.13948i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(1.26839 + 0.815148i) q^{10} +(-0.650933 + 4.52734i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(0.448802 + 0.288428i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(0.626339 + 1.37149i) q^{15} +(0.841254 - 0.540641i) q^{16} +(1.56321 + 0.458999i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.620628 - 0.182233i) q^{19} +(0.626339 - 1.37149i) q^{20} +(-0.142315 - 0.989821i) q^{21} +4.57389 q^{22} +(-0.679686 + 4.74742i) q^{23} +1.00000 q^{24} +(0.388051 + 2.69896i) q^{25} +(0.221621 - 0.485282i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(6.91617 + 2.03077i) q^{29} +(1.26839 - 0.815148i) q^{30} +(0.297002 + 0.650345i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(3.84780 + 2.47283i) q^{33} +(0.231859 - 1.61262i) q^{34} +(-0.214574 + 1.49240i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-1.04691 - 1.20820i) q^{37} +(-0.268702 - 0.588376i) q^{38} +(0.448802 - 0.288428i) q^{39} +(-1.44667 - 0.424780i) q^{40} +(-0.692975 + 0.799736i) q^{41} +(-0.959493 + 0.281733i) q^{42} +(1.60546 - 3.51547i) q^{43} +(-0.650933 - 4.52734i) q^{44} +1.50774 q^{45} +(4.79583 - 0.00286106i) q^{46} +9.54327 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(2.61626 - 0.768203i) q^{50} +(1.06690 - 1.23127i) q^{51} +(-0.511882 - 0.150302i) q^{52} +(-2.74627 + 1.76492i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-4.51609 - 5.21185i) q^{55} +(0.841254 + 0.540641i) q^{56} +(0.0920533 - 0.640245i) q^{57} +(1.02583 - 7.13479i) q^{58} +(9.57690 + 6.15470i) q^{59} +(-0.987362 - 1.13948i) q^{60} +(1.50935 + 3.30502i) q^{61} +(0.601457 - 0.386533i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.771787 + 0.226617i) q^{65} +(1.90006 - 4.16056i) q^{66} +(-0.277422 - 1.92951i) q^{67} -1.62920 q^{68} +(4.03606 + 2.59041i) q^{69} +1.50774 q^{70} +(-0.0910965 - 0.633590i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-4.14061 + 1.21579i) q^{73} +(-1.04691 + 1.20820i) q^{74} +(2.61626 + 0.768203i) q^{75} +(-0.544147 + 0.349702i) q^{76} +(1.90006 + 4.16056i) q^{77} +(-0.349363 - 0.403186i) q^{78} +(-3.05452 - 1.96302i) q^{79} +(-0.214574 + 1.49240i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.890217 + 0.572108i) q^{82} +(-2.89602 - 3.34219i) q^{83} +(0.415415 + 0.909632i) q^{84} +(-2.06647 + 1.32804i) q^{85} +(-3.70817 - 1.08882i) q^{86} +(4.72034 - 5.44756i) q^{87} +(-4.38862 + 1.28861i) q^{88} +(-3.97803 + 8.71067i) q^{89} +(-0.214574 - 1.49240i) q^{90} +0.533492 q^{91} +(-0.685350 - 4.74661i) q^{92} +0.714954 q^{93} +(-1.35815 - 9.44613i) q^{94} +(-0.405134 + 0.887120i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(6.30137 - 7.27217i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(3.84780 - 2.47283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.987362	+	1.13948i	−0.441562	+	0.509589i	−0.932284	−	0.361727i	$-0.882187\pi$
$5$	−0.987362	+	1.13948i	−0.441562	+	0.509589i	0.490723	+	0.871316i	$0.336733\pi$
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	1.26839	+	0.815148i	0.401102	+	0.257772i
$11$	−0.650933	+	4.52734i	−0.196264	+	1.36504i	0.618743	+	0.785593i	$0.287642\pi$
$11$	−0.650933	+	4.52734i	−0.196264	+	1.36504i	−0.815007	+	0.579451i	$0.803267\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	0.448802	+	0.288428i	0.124475	+	0.0799954i	0.601397	−	0.798950i	$-0.294611\pi$
$13$	0.448802	+	0.288428i	0.124475	+	0.0799954i	−0.476922	+	0.878946i	$0.658247\pi$
$14$	−0.654861	−	0.755750i	−0.175019	−	0.201983i
$15$	0.626339	+	1.37149i	0.161720	+	0.354118i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	1.56321	+	0.458999i	0.379133	+	0.111324i	0.465746	−	0.884919i	$-0.345786\pi$
$17$	1.56321	+	0.458999i	0.379133	+	0.111324i	−0.0866127	+	0.996242i	$0.527604\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	0.620628	−	0.182233i	0.142382	−	0.0418071i	−0.209765	−	0.977752i	$-0.567270\pi$
$19$	0.620628	−	0.182233i	0.142382	−	0.0418071i	0.352147	+	0.935945i	$0.385452\pi$
$20$	0.626339	−	1.37149i	0.140054	−	0.306675i
$21$	−0.142315	−	0.989821i	−0.0310556	−	0.215997i
$22$	4.57389			0.975158
$23$	−0.679686	+	4.74742i	−0.141724	+	0.989906i
$23$	−0.679686	+	4.74742i	−0.141724	+	0.989906i
$24$	1.00000			0.204124
$25$	0.388051	+	2.69896i	0.0776102	+	0.539791i
$26$	0.221621	−	0.485282i	0.0434634	−	0.0951715i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	−0.654861	+	0.755750i	−0.123757	+	0.142823i
$29$	6.91617	+	2.03077i	1.28430	+	0.377105i	0.851486	−	0.524378i	$-0.175702\pi$
$29$	6.91617	+	2.03077i	1.28430	+	0.377105i	0.432816	+	0.901483i	$0.357520\pi$
$30$	1.26839	−	0.815148i	0.231576	−	0.148825i
$31$	0.297002	+	0.650345i	0.0533432	+	0.116805i	0.934427	−	0.356155i	$-0.115913\pi$
$31$	0.297002	+	0.650345i	0.0533432	+	0.116805i	−0.881084	+	0.472961i	$0.843185\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	3.84780	+	2.47283i	0.669817	+	0.430465i
$34$	0.231859	−	1.61262i	0.0397635	−	0.276562i
$35$	−0.214574	+	1.49240i	−0.0362697	+	0.252261i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−1.04691	−	1.20820i	−0.172111	−	0.198627i	0.663140	−	0.748495i	$-0.269223\pi$
$37$	−1.04691	−	1.20820i	−0.172111	−	0.198627i	−0.835251	+	0.549868i	$0.814678\pi$
$38$	−0.268702	−	0.588376i	−0.0435893	−	0.0954472i
$39$	0.448802	−	0.288428i	0.0718659	−	0.0461854i
$40$	−1.44667	−	0.424780i	−0.228738	−	0.0671637i
$41$	−0.692975	+	0.799736i	−0.108225	+	0.124898i	−0.807277	−	0.590172i	$-0.799060\pi$
$41$	−0.692975	+	0.799736i	−0.108225	+	0.124898i	0.699053	+	0.715070i	$0.253605\pi$
$42$	−0.959493	+	0.281733i	−0.148053	+	0.0434723i
$43$	1.60546	−	3.51547i	0.244831	−	0.536104i	−0.746825	−	0.665021i	$-0.768423\pi$
$43$	1.60546	−	3.51547i	0.244831	−	0.536104i	0.991655	+	0.128917i	$0.0411499\pi$
$44$	−0.650933	−	4.52734i	−0.0981318	−	0.682522i
$45$	1.50774			0.224761
$46$	4.79583	−	0.00286106i	0.707107	−	0.000421840i
$47$	9.54327			1.39203			0.696014	−	0.718028i	$-0.254955\pi$
$47$	9.54327			1.39203			0.696014	+	0.718028i	$0.254955\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	2.61626	−	0.768203i	0.369995	−	0.108640i
$51$	1.06690	−	1.23127i	0.149396	−	0.172412i
$52$	−0.511882	−	0.150302i	−0.0709853	−	0.0208432i
$53$	−2.74627	+	1.76492i	−0.377229	+	0.242430i	−0.715491	−	0.698621i	$-0.753797\pi$
$53$	−2.74627	+	1.76492i	−0.377229	+	0.242430i	0.338263	+	0.941052i	$0.390161\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−4.51609	−	5.21185i	−0.608949	−	0.702765i
$56$	0.841254	+	0.540641i	0.112417	+	0.0722462i
$57$	0.0920533	−	0.640245i	0.0121928	−	0.0848025i
$58$	1.02583	−	7.13479i	0.134698	−	0.936843i
$59$	9.57690	+	6.15470i	1.24681	+	0.801274i	0.986422	−	0.164231i	$-0.0525144\pi$
$59$	9.57690	+	6.15470i	1.24681	+	0.801274i	0.260384	+	0.965505i	$0.416151\pi$
$60$	−0.987362	−	1.13948i	−0.127468	−	0.147106i
$61$	1.50935	+	3.30502i	0.193253	+	0.423165i	0.981309	−	0.192439i	$-0.0616396\pi$
$61$	1.50935	+	3.30502i	0.193253	+	0.423165i	−0.788056	+	0.615603i	$0.788912\pi$
$62$	0.601457	−	0.386533i	0.0763851	−	0.0490898i
$63$	−0.959493	−	0.281733i	−0.120885	−	0.0354950i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−0.771787	+	0.226617i	−0.0957284	+	0.0281084i
$66$	1.90006	−	4.16056i	0.233882	−	0.512130i
$67$	−0.277422	−	1.92951i	−0.0338925	−	0.235728i	0.965833	−	0.259166i	$-0.0834477\pi$
$67$	−0.277422	−	1.92951i	−0.0338925	−	0.235728i	−0.999725	+	0.0234385i	$0.992539\pi$
$68$	−1.62920			−0.197570
$69$	4.03606	+	2.59041i	0.485884	+	0.311849i
$70$	1.50774			0.180210
$71$	−0.0910965	−	0.633590i	−0.0108112	−	0.0751933i	0.983702	−	0.179809i	$-0.0575479\pi$
$71$	−0.0910965	−	0.633590i	−0.0108112	−	0.0751933i	−0.994513	+	0.104615i	$0.966639\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	−4.14061	+	1.21579i	−0.484622	+	0.142298i	−0.514911	−	0.857243i	$-0.672175\pi$
$73$	−4.14061	+	1.21579i	−0.484622	+	0.142298i	0.0302897	+	0.999541i	$0.490357\pi$
$74$	−1.04691	+	1.20820i	−0.121701	+	0.140450i
$75$	2.61626	+	0.768203i	0.302100	+	0.0887044i
$76$	−0.544147	+	0.349702i	−0.0624179	+	0.0401136i
$77$	1.90006	+	4.16056i	0.216532	+	0.474140i
$78$	−0.349363	−	0.403186i	−0.0395576	−	0.0456519i
$79$	−3.05452	−	1.96302i	−0.343660	−	0.220857i	0.357413	−	0.933947i	$-0.383659\pi$
$79$	−3.05452	−	1.96302i	−0.343660	−	0.220857i	−0.701073	+	0.713090i	$0.747295\pi$
$80$	−0.214574	+	1.49240i	−0.0239901	+	0.166855i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	0.890217	+	0.572108i	0.0983080	+	0.0631787i
$83$	−2.89602	−	3.34219i	−0.317880	−	0.366853i	0.574212	−	0.818706i	$-0.305308\pi$
$83$	−2.89602	−	3.34219i	−0.317880	−	0.366853i	−0.892092	+	0.451854i	$0.850763\pi$
$84$	0.415415	+	0.909632i	0.0453255	+	0.0992490i
$85$	−2.06647	+	1.32804i	−0.224140	+	0.144046i
$86$	−3.70817	−	1.08882i	−0.399862	−	0.117410i
$87$	4.72034	−	5.44756i	0.506073	−	0.584040i
$88$	−4.38862	+	1.28861i	−0.467828	+	0.137367i
$89$	−3.97803	+	8.71067i	−0.421670	+	0.923329i	0.572936	+	0.819600i	$0.305805\pi$
$89$	−3.97803	+	8.71067i	−0.421670	+	0.923329i	−0.994606	+	0.103728i	$0.966923\pi$
$90$	−0.214574	−	1.49240i	−0.0226181	−	0.157312i
$91$	0.533492			0.0559252
$92$	−0.685350	−	4.74661i	−0.0714527	−	0.494868i
$93$	0.714954			0.0741372
$94$	−1.35815	−	9.44613i	−0.140082	−	0.974294i
$95$	−0.405134	+	0.887120i	−0.0415659	+	0.0910166i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	6.30137	−	7.27217i	0.639807	−	0.738377i	−0.339534	−	0.940594i	$-0.610269\pi$
$97$	6.30137	−	7.27217i	0.639807	−	0.738377i	0.979341	+	0.202217i	$0.0648147\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	3.84780	−	2.47283i	0.386719	−	0.248529i
$100$	−1.13272	−	2.48030i	−0.113272	−	0.248030i
$101$	3.30032	+	3.80878i	0.328395	+	0.378988i	0.895805	−	0.444448i	$-0.146600\pi$
$101$	3.30032	+	3.80878i	0.328395	+	0.378988i	−0.567410	+	0.823435i	$0.692055\pi$
$102$	−1.37057	−	0.880812i	−0.135707	−	0.0872134i
$103$	0.412608	−	2.86975i	0.0406554	−	0.282765i	−0.959344	−	0.282238i	$-0.908923\pi$
$103$	0.412608	−	2.86975i	0.0406554	−	0.282765i	1.00000		0.000526795i	$-0.000167684\pi$
$104$	−0.0759239	+	0.528062i	−0.00744495	+	0.0517807i
$105$	1.26839	+	0.815148i	0.123783	+	0.0795503i
$106$	2.13779	+	2.46714i	0.207640	+	0.239630i
$107$	4.01213	+	8.78535i	0.387868	+	0.849311i	0.998358	+	0.0572876i	$0.0182452\pi$
$107$	4.01213	+	8.78535i	0.387868	+	0.849311i	−0.610490	+	0.792024i	$0.709028\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	−15.5340	−	4.56121i	−1.48789	−	0.436884i	−0.566024	−	0.824389i	$-0.691519\pi$
$109$	−15.5340	−	4.56121i	−1.48789	−	0.436884i	−0.921868	+	0.387504i	$0.873337\pi$
$110$	−4.51609	+	5.21185i	−0.430592	+	0.496930i
$111$	−1.53392	+	0.450399i	−0.145593	+	0.0427500i
$112$	0.415415	−	0.909632i	0.0392530	−	0.0859521i
$113$	−1.87251	−	13.0236i	−0.176151	−	1.22516i	−0.865568	−	0.500791i	$-0.833042\pi$
$113$	−1.87251	−	13.0236i	−0.176151	−	1.22516i	0.689417	−	0.724365i	$-0.257867\pi$
$114$	−0.646829			−0.0605811
$115$	−4.73848	−	5.46191i	−0.441866	−	0.509326i
$116$	−7.20816			−0.669260
$117$	−0.0759239	−	0.528062i	−0.00701916	−	0.0488193i
$118$	4.72912	−	10.3553i	0.435351	−	0.953285i
$119$	1.56321	−	0.458999i	0.143299	−	0.0420763i
$120$	−0.987362	+	1.13948i	−0.0901334	+	0.104019i
$121$	−9.51866	−	2.79493i	−0.865333	−	0.254085i
$122$	3.05658	−	1.96434i	0.276730	−	0.177843i
$123$	0.439593	+	0.962575i	0.0396368	+	0.0867925i
$124$	−0.468195	−	0.540326i	−0.0420452	−	0.0485227i
$125$	−9.80052	−	6.29841i	−0.876585	−	0.563347i
$126$	−0.142315	+	0.989821i	−0.0126784	+	0.0881803i
$127$	−0.730833	+	5.08306i	−0.0648510	+	0.451048i	0.931361	+	0.364096i	$0.118622\pi$
$127$	−0.730833	+	5.08306i	−0.0648510	+	0.451048i	−0.996212	+	0.0869526i	$0.972287\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−2.53085	−	2.92076i	−0.222829	−	0.257158i
$130$	0.334147	+	0.731680i	0.0293066	+	0.0641726i
$131$	0.0890996	−	0.0572608i	0.00778466	−	0.00500290i	−0.536743	−	0.843746i	$-0.680345\pi$
$131$	0.0890996	−	0.0572608i	0.00778466	−	0.00500290i	0.544527	+	0.838743i	$0.316709\pi$
$132$	−4.38862	−	1.28861i	−0.381980	−	0.112160i
$133$	0.423583	−	0.488841i	0.0367293	−	0.0423879i
$134$	−1.87039	+	0.549197i	−0.161577	+	0.0474434i
$135$	0.626339	−	1.37149i	0.0539067	−	0.118039i
$136$	0.231859	+	1.61262i	0.0198818	+	0.138281i
$137$	−9.90231			−0.846012			−0.423006	−	0.906127i	$-0.639025\pi$
$137$	−9.90231			−0.846012			−0.423006	+	0.906127i	$0.639025\pi$
$138$	1.98966	−	4.36363i	0.169371	−	0.371457i
$139$	15.6893			1.33074			0.665372	−	0.746512i	$-0.268273\pi$
$139$	15.6893			1.33074			0.665372	+	0.746512i	$0.268273\pi$
$140$	−0.214574	−	1.49240i	−0.0181348	−	0.126131i
$141$	3.96442	−	8.68086i	0.333864	−	0.731060i
$142$	−0.614177	+	0.180339i	−0.0515406	+	0.0151337i
$143$	−1.59795	+	1.84413i	−0.133627	+	0.154214i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−9.14278	+	5.87571i	−0.759267	+	0.487951i
$146$	1.79269	+	3.92544i	0.148364	+	0.324872i
$147$	−0.654861	−	0.755750i	−0.0540120	−	0.0623332i
$148$	1.34489	+	0.864310i	0.110549	+	0.0710458i
$149$	−1.89535	+	13.1825i	−0.155274	+	1.07995i	0.751925	+	0.659248i	$0.229125\pi$
$149$	−1.89535	+	13.1825i	−0.155274	+	1.07995i	−0.907199	+	0.420702i	$0.861784\pi$
$150$	0.388051	−	2.69896i	0.0316843	−	0.220369i
$151$	11.4138	+	7.33522i	0.928843	+	0.596931i	0.915211	−	0.402976i	$-0.132024\pi$
$151$	11.4138	+	7.33522i	0.928843	+	0.596931i	0.0136326	+	0.999907i	$0.495660\pi$
$152$	0.423583	+	0.488841i	0.0343571	+	0.0396502i
$153$	−0.676794	−	1.48197i	−0.0547156	−	0.119810i
$154$	3.84780	−	2.47283i	0.310065	−	0.199267i
$155$	−1.03430	−	0.303698i	−0.0830771	−	0.0243936i
$156$	−0.349363	+	0.403186i	−0.0279714	+	0.0322808i
$157$	1.11018	−	0.325978i	0.0886020	−	0.0260159i	−0.237131	−	0.971478i	$-0.576207\pi$
$157$	1.11018	−	0.325978i	0.0886020	−	0.0260159i	0.325733	+	0.945462i	$0.394389\pi$
$158$	−1.50834	+	3.30280i	−0.119997	+	0.262756i
$159$	0.464586	+	3.23127i	0.0368441	+	0.256256i
$160$	1.50774			0.119198
$161$	1.99486	+	4.36125i	0.157217	+	0.343715i
$162$	1.00000			0.0785674
$163$	0.0304894	+	0.212059i	0.00238812	+	0.0166097i	0.990981	−	0.134005i	$-0.0427838\pi$
$163$	0.0304894	+	0.212059i	0.00238812	+	0.0166097i	−0.988593	+	0.150615i	$0.951875\pi$
$164$	0.439593	−	0.962575i	0.0343265	−	0.0751645i
$165$	−6.61691	+	1.94290i	−0.515126	+	0.151255i
$166$	−2.89602	+	3.34219i	−0.224775	+	0.259404i
$167$	6.25781	+	1.83746i	0.484244	+	0.142187i	0.514737	−	0.857348i	$-0.327890\pi$
$167$	6.25781	+	1.83746i	0.484244	+	0.142187i	−0.0304931	+	0.999535i	$0.509708\pi$
$168$	0.841254	−	0.540641i	0.0649041	−	0.0417113i
$169$	−5.28216	−	11.5663i	−0.406320	−	0.889717i
$170$	1.60861	+	1.85643i	0.123375	+	0.142382i
$171$	−0.544147	−	0.349702i	−0.0416120	−	0.0267424i
$172$	−0.550007	+	3.82538i	−0.0419376	+	0.291683i
$173$	−0.445673	+	3.09972i	−0.0338839	+	0.235667i	−0.999725	−	0.0234691i	$-0.992529\pi$
$173$	−0.445673	+	3.09972i	−0.0338839	+	0.235667i	0.965841	+	0.259137i	$0.0834380\pi$
$174$	−6.06389	−	3.89702i	−0.459702	−	0.295433i
$175$	1.78562	+	2.06071i	0.134980	+	0.155775i
$176$	1.90006	+	4.16056i	0.143223	+	0.313614i
$177$	9.57690	−	6.15470i	0.719844	−	0.462616i
$178$	9.18814	+	2.69788i	0.688680	+	0.202215i
$179$	−15.0133	+	17.3263i	−1.12215	+	1.29503i	−0.171351	+	0.985210i	$0.554813\pi$
$179$	−15.0133	+	17.3263i	−1.12215	+	1.29503i	−0.950796	+	0.309817i	$0.899732\pi$
$180$	−1.44667	+	0.424780i	−0.107828	+	0.0316613i
$181$	−5.61319	+	12.2912i	−0.417225	+	0.913596i	0.578004	+	0.816034i	$0.303832\pi$
$181$	−5.61319	+	12.2912i	−0.417225	+	0.913596i	−0.995229	+	0.0975621i	$0.968896\pi$
$182$	−0.0759239	−	0.528062i	−0.00562785	−	0.0391426i
$183$	3.63336			0.268586
$184$	−4.60076	+	1.35389i	−0.339173	+	0.0998099i
$185$	2.41039			0.177216
$186$	−0.101749	−	0.707676i	−0.00746056	−	0.0518894i
$187$	−3.09558	+	6.77838i	−0.226372	+	0.495685i
$188$	−9.15670	+	2.68865i	−0.667821	+	0.196090i
$189$	−0.654861	+	0.755750i	−0.0476341	+	0.0549727i
$190$	0.935747	+	0.274760i	0.0678862	+	0.0199332i
$191$	−14.9036	+	9.57793i	−1.07838	+	0.693035i	−0.954183	−	0.299222i	$-0.903273\pi$
$191$	−14.9036	+	9.57793i	−1.07838	+	0.693035i	−0.124200	+	0.992257i	$0.539636\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	−5.12103	−	5.90998i	−0.368620	−	0.425410i	0.540889	−	0.841094i	$-0.318088\pi$
$193$	−5.12103	−	5.90998i	−0.368620	−	0.425410i	−0.909509	+	0.415684i	$0.863542\pi$
$194$	−8.09492	−	5.20229i	−0.581182	−	0.373503i
$195$	−0.114474	+	0.796182i	−0.00819763	+	0.0570158i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	9.92101	+	6.37585i	0.706843	+	0.454260i	0.844038	−	0.536284i	$-0.180172\pi$
$197$	9.92101	+	6.37585i	0.706843	+	0.454260i	−0.137195	+	0.990544i	$0.543809\pi$
$198$	−2.99526	−	3.45672i	−0.212864	−	0.245658i
$199$	1.22926	+	2.69170i	0.0871397	+	0.190809i	0.948185	−	0.317719i	$-0.102917\pi$
$199$	1.22926	+	2.69170i	0.0871397	+	0.190809i	−0.861045	+	0.508528i	$0.830190\pi$
$200$	−2.29385	+	1.47417i	−0.162200	+	0.104240i
$201$	−1.87039	−	0.549197i	−0.131927	−	0.0387374i
$202$	3.30032	−	3.80878i	0.232210	−	0.267985i
$203$	6.91617	−	2.03077i	0.485420	−	0.142532i
$204$	−0.676794	+	1.48197i	−0.0473851	+	0.103759i
$205$	−0.227063	−	1.57926i	−0.0158588	−	0.110300i
$206$	−2.89926			−0.202001
$207$	4.03296	−	2.59523i	0.280310	−	0.180381i
$208$	0.533492			0.0369910
$209$	0.421042	+	2.92841i	0.0291241	+	0.202563i
$210$	0.626339	−	1.37149i	0.0432215	−	0.0946419i
$211$	−3.79365	+	1.11391i	−0.261165	+	0.0766851i	−0.409694	−	0.912223i	$-0.634364\pi$
$211$	−3.79365	+	1.11391i	−0.261165	+	0.0766851i	0.148529	+	0.988908i	$0.452546\pi$
$212$	2.13779	−	2.46714i	0.146824	−	0.169444i
$213$	−0.614177	−	0.180339i	−0.0420827	−	0.0123566i
$214$	8.12494	−	5.22158i	0.555409	−	0.356940i
$215$	2.42062	+	5.30043i	0.165085	+	0.361486i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	0.601457	+	0.386533i	0.0408296	+	0.0262396i
$218$	−2.30406	+	16.0251i	−0.156050	+	1.08535i
$219$	−0.614148	+	4.27149i	−0.0415002	+	0.288641i
$220$	5.80150	+	3.72840i	0.391137	+	0.251369i
$221$	0.569182	+	0.656871i	0.0382873	+	0.0441859i
$222$	0.664114	+	1.45421i	0.0445724	+	0.0976000i
$223$	19.1269	−	12.2921i	1.28083	−	0.823139i	0.289839	−	0.957075i	$-0.406398\pi$
$223$	19.1269	−	12.2921i	1.28083	−	0.823139i	0.990990	+	0.133937i	$0.0427619\pi$
$224$	−0.959493	−	0.281733i	−0.0641088	−	0.0188240i
$225$	1.78562	−	2.06071i	0.119041	−	0.137381i
$226$	−12.6245	+	3.70690i	−0.839772	+	0.246579i
$227$	−10.0037	+	21.9050i	−0.663967	+	1.45389i	0.214811	+	0.976656i	$0.431087\pi$
$227$	−10.0037	+	21.9050i	−0.663967	+	1.45389i	−0.878778	+	0.477230i	$0.841641\pi$
$228$	0.0920533	+	0.640245i	0.00609638	+	0.0424013i
$229$	2.23044			0.147392			0.0736959	−	0.997281i	$-0.476521\pi$
$229$	2.23044			0.147392			0.0736959	+	0.997281i	$0.476521\pi$
$230$	−4.73196	+	5.46756i	−0.312016	+	0.360520i
$231$	4.57389			0.300940
$232$	1.02583	+	7.13479i	0.0673489	+	0.468422i
$233$	6.32183	−	13.8429i	0.414157	−	0.906877i	−0.581480	−	0.813561i	$-0.697526\pi$
$233$	6.32183	−	13.8429i	0.414157	−	0.906877i	0.995637	−	0.0933160i	$-0.0297467\pi$
$234$	−0.511882	+	0.150302i	−0.0334628	+	0.00982556i
$235$	−9.42266	+	10.8743i	−0.614667	+	0.709363i
$236$	−10.9229	−	3.20727i	−0.711023	−	0.208775i
$237$	−3.05452	+	1.96302i	−0.198412	+	0.127512i
$238$	−0.676794	−	1.48197i	−0.0438700	−	0.0960620i
$239$	−16.1399	−	18.6265i	−1.04401	−	1.20485i	−0.978340	−	0.207006i	$-0.933628\pi$
$239$	−16.1399	−	18.6265i	−1.04401	−	1.20485i	−0.0656668	−	0.997842i	$-0.520917\pi$
$240$	1.26839	+	0.815148i	0.0818745	+	0.0526176i
$241$	0.485748	−	3.37845i	0.0312898	−	0.217625i	−0.968177	−	0.250265i	$-0.919482\pi$
$241$	0.485748	−	3.37845i	0.0312898	−	0.217625i	0.999467	+	0.0326397i	$0.0103914\pi$
$242$	−1.41184	+	9.81953i	−0.0907562	+	0.631224i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−2.37935	−	2.74591i	−0.152322	−	0.175789i
$245$	0.626339	+	1.37149i	0.0400153	+	0.0876214i
$246$	0.890217	−	0.572108i	0.0567581	−	0.0364762i
$247$	0.331100	+	0.0972197i	0.0210674	+	0.00618594i
$248$	−0.468195	+	0.540326i	−0.0297304	+	0.0343107i
$249$	−4.24321	+	1.24592i	−0.268903	+	0.0789570i
$250$	−4.83954	+	10.5971i	−0.306079	+	0.670221i
$251$	−3.75663	−	26.1279i	−0.237116	−	1.64918i	−0.666097	−	0.745865i	$-0.732036\pi$
$251$	−3.75663	−	26.1279i	−0.237116	−	1.64918i	0.428981	−	0.903313i	$-0.358873\pi$
$252$	1.00000			0.0629941
$253$	−21.0508	−	6.16742i	−1.32345	−	0.387743i
$254$	5.13533			0.322219
$255$	0.349584	+	2.43141i	0.0218918	+	0.152261i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−10.8096	+	3.17399i	−0.674286	+	0.197988i	−0.600911	−	0.799316i	$-0.705195\pi$
$257$	−10.8096	+	3.17399i	−0.674286	+	0.197988i	−0.0733752	+	0.997304i	$0.523377\pi$
$258$	−2.53085	+	2.92076i	−0.157564	+	0.181838i
$259$	−1.53392	−	0.450399i	−0.0953131	−	0.0279864i
$260$	0.676679	−	0.434875i	0.0419658	−	0.0269698i
$261$	−2.99438	−	6.55677i	−0.185347	−	0.405854i
$262$	−0.0693582	−	0.0800436i	−0.00428496	−	0.00494511i
$263$	−1.69625	−	1.09012i	−0.104596	−	0.0672195i	0.487297	−	0.873236i	$-0.337983\pi$
$263$	−1.69625	−	1.09012i	−0.104596	−	0.0672195i	−0.591893	+	0.806017i	$0.701619\pi$
$264$	−0.650933	+	4.52734i	−0.0400622	+	0.278638i
$265$	0.700477	−	4.87192i	0.0430299	−	0.299280i
$266$	−0.544147	−	0.349702i	−0.0333638	−	0.0214416i
$267$	6.27097	+	7.23708i	0.383777	+	0.442902i
$268$	0.809792	+	1.77320i	0.0494659	+	0.108315i
$269$	−2.96607	+	1.90618i	−0.180845	+	0.116222i	−0.627931	−	0.778269i	$-0.716098\pi$
$269$	−2.96607	+	1.90618i	−0.180845	+	0.116222i	0.447086	+	0.894491i	$0.352462\pi$
$270$	−1.44667	−	0.424780i	−0.0880415	−	0.0258513i
$271$	−2.79957	+	3.23087i	−0.170061	+	0.196261i	−0.834382	−	0.551186i	$-0.814175\pi$
$271$	−2.79957	+	3.23087i	−0.170061	+	0.196261i	0.664321	+	0.747448i	$0.268721\pi$
$272$	1.56321	−	0.458999i	0.0947833	−	0.0278309i
$273$	0.221621	−	0.485282i	0.0134131	−	0.0293706i
$274$	1.40925	+	9.80152i	0.0851357	+	0.592132i
$275$	−12.4717			−0.752071
$276$	−4.60237	−	1.34840i	−0.277030	−	0.0811639i
$277$	−1.72957			−0.103920			−0.0519599	−	0.998649i	$-0.516547\pi$
$277$	−1.72957			−0.103920			−0.0519599	+	0.998649i	$0.516547\pi$
$278$	−2.23281	−	15.5296i	−0.133915	−	0.931401i
$279$	0.297002	−	0.650345i	0.0177811	−	0.0389351i
$280$	−1.44667	+	0.424780i	−0.0864550	+	0.0253855i
$281$	16.7460	−	19.3260i	0.998985	−	1.15289i	0.0107510	−	0.999942i	$-0.496578\pi$
$281$	16.7460	−	19.3260i	0.998985	−	1.15289i	0.988234	−	0.152948i	$-0.0488768\pi$
$282$	−9.15670	−	2.68865i	−0.545273	−	0.160107i
$283$	14.2895	−	9.18332i	0.849424	−	0.545892i	−0.0419709	−	0.999119i	$-0.513364\pi$
$283$	14.2895	−	9.18332i	0.849424	−	0.545892i	0.891395	+	0.453227i	$0.149727\pi$
$284$	0.265910	+	0.582261i	0.0157788	+	0.0345508i
$285$	0.638654	+	0.737046i	0.0378306	+	0.0436588i
$286$	2.05277	+	1.31924i	0.121383	+	0.0780082i
$287$	−0.150598	+	1.04743i	−0.00888951	+	0.0618279i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	−12.0684	−	7.75588i	−0.709905	−	0.456228i
$290$	7.11706	+	8.21352i	0.417928	+	0.482315i
$291$	−3.99731	−	8.75289i	−0.234327	−	0.513104i
$292$	3.63036	−	2.33309i	0.212451	−	0.136534i
$293$	−4.68431	−	1.37544i	−0.273660	−	0.0803539i	0.142023	−	0.989863i	$-0.454639\pi$
$293$	−4.68431	−	1.37544i	−0.273660	−	0.0803539i	−0.415683	+	0.909509i	$0.636457\pi$
$294$	−0.654861	+	0.755750i	−0.0381923	+	0.0440762i
$295$	−16.4690	+	4.83574i	−0.958862	+	0.281547i
$296$	0.664114	−	1.45421i	0.0386009	−	0.0845241i
$297$	−0.650933	−	4.52734i	−0.0377710	−	0.262703i
$298$	13.3180			0.771493
$299$	−1.67433	+	1.93461i	−0.0968292	+	0.111882i
$300$	−2.72671			−0.157427
$301$	−0.550007	−	3.82538i	−0.0317019	−	0.220491i
$302$	5.63620	−	12.3416i	0.324327	−	0.710176i
$303$	4.83559	−	1.41986i	0.277797	−	0.0815687i
$304$	0.423583	−	0.488841i	0.0242941	−	0.0280369i
$305$	−5.25627	−	1.54338i	−0.300973	−	0.0883737i
$306$	−1.37057	+	0.880812i	−0.0783503	+	0.0503527i
$307$	0.748246	+	1.63843i	0.0427046	+	0.0935101i	0.929782	−	0.368111i	$-0.119995\pi$
$307$	0.748246	+	1.63843i	0.0427046	+	0.0935101i	−0.887077	+	0.461621i	$0.847268\pi$
$308$	−2.99526	−	3.45672i	−0.170671	−	0.196965i
$309$	−2.43901	−	1.56746i	−0.138751	−	0.0891696i
$310$	−0.153411	+	1.06699i	−0.00871314	+	0.0606012i
$311$	−2.11992	+	14.7443i	−0.120209	+	0.836075i	0.837108	+	0.547037i	$0.184244\pi$
$311$	−2.11992	+	14.7443i	−0.120209	+	0.836075i	−0.957318	+	0.289038i	$0.906665\pi$
$312$	0.448802	+	0.288428i	0.0254084	+	0.0163290i
$313$	−3.86487	−	4.46030i	−0.218456	−	0.252111i	0.635935	−	0.771743i	$-0.280615\pi$
$313$	−3.86487	−	4.46030i	−0.218456	−	0.252111i	−0.854390	+	0.519632i	$0.826069\pi$
$314$	−0.480655	−	1.05249i	−0.0271249	−	0.0593954i
$315$	1.26839	−	0.815148i	0.0714659	−	0.0459284i
$316$	3.48384	+	1.02295i	0.195981	+	0.0575452i
$317$	0.689457	−	0.795675i	0.0387237	−	0.0446896i	−0.736057	−	0.676919i	$-0.763315\pi$
$317$	0.689457	−	0.795675i	0.0387237	−	0.0446896i	0.774781	+	0.632230i	$0.217860\pi$
$318$	3.13226	−	0.919715i	0.175648	−	0.0515750i
$319$	−13.6960	+	29.9900i	−0.766827	+	1.67912i
$320$	−0.214574	−	1.49240i	−0.0119951	−	0.0834275i
$321$	9.65813			0.539064
$322$	4.03296	−	2.59523i	0.224748	−	0.144626i
$323$	1.05381			0.0586357
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−0.604295	+	1.32322i	−0.0335203	+	0.0733991i
$326$	0.205561	−	0.0603582i	0.0113850	−	0.00334293i
$327$	−10.6021	+	12.2355i	−0.586297	+	0.676623i
$328$	−1.01534	−	0.298130i	−0.0560627	−	0.0164615i
$329$	8.02831	−	5.15948i	0.442615	−	0.284451i
$330$	2.86481	+	6.27306i	0.157703	+	0.345320i
$331$	1.88145	+	2.17131i	0.103414	+	0.119346i	0.805097	−	0.593143i	$-0.202113\pi$
$331$	1.88145	+	2.17131i	0.103414	+	0.119346i	−0.701683	+	0.712489i	$0.747568\pi$
$332$	3.72032	+	2.39090i	0.204179	+	0.131218i
$333$	−0.227515	+	1.58240i	−0.0124678	+	0.0867152i
$334$	0.928177	−	6.45561i	0.0507876	−	0.353235i
$335$	2.47255	+	1.58901i	0.135090	+	0.0868170i
$336$	−0.654861	−	0.755750i	−0.0357256	−	0.0412295i
$337$	−8.10377	−	17.7448i	−0.441440	−	0.966620i	−0.991332	−	0.131383i	$-0.958058\pi$
$337$	−8.10377	−	17.7448i	−0.441440	−	0.966620i	0.549891	−	0.835236i	$-0.314669\pi$
$338$	−10.6969	+	6.87446i	−0.581833	+	0.373921i
$339$	−12.6245	−	3.70690i	−0.685671	−	0.201331i
$340$	1.60861	−	1.85643i	0.0872391	−	0.100679i
$341$	−3.13766	+	0.921300i	−0.169914	+	0.0498912i
$342$	−0.268702	+	0.588376i	−0.0145298	+	0.0318157i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	3.86472			0.208372
$345$	−6.93677	+	2.04131i	−0.373463	+	0.109901i
$346$	3.13160			0.168356
$347$	1.78380	+	12.4066i	0.0957594	+	0.666022i	0.980001	+	0.198992i	$0.0637668\pi$
$347$	1.78380	+	12.4066i	0.0957594	+	0.666022i	−0.884242	+	0.467030i	$0.845324\pi$
$348$	−2.99438	+	6.55677i	−0.160515	+	0.351480i
$349$	24.7554	−	7.26884i	1.32513	−	0.389092i	0.458785	−	0.888547i	$-0.348285\pi$
$349$	24.7554	−	7.26884i	1.32513	−	0.389092i	0.866340	+	0.499455i	$0.166466\pi$
$350$	1.78562	−	2.06071i	0.0954451	−	0.110150i
$351$	−0.511882	−	0.150302i	−0.0273222	−	0.00802253i
$352$	3.84780	−	2.47283i	0.205089	−	0.131802i
$353$	−10.9776	−	24.0376i	−0.584280	−	1.27939i	−0.938838	−	0.344360i	$-0.888096\pi$
$353$	−10.9776	−	24.0376i	−0.584280	−	1.27939i	0.354558	−	0.935034i	$-0.384631\pi$
$354$	−7.45499	−	8.60352i	−0.396228	−	0.457272i
$355$	0.811907	+	0.521781i	0.0430915	+	0.0276932i
$356$	1.36281	−	9.47856i	0.0722289	−	0.502363i
$357$	0.231859	−	1.61262i	0.0122713	−	0.0853487i
$358$	19.2865	+	12.3947i	1.01933	+	0.655081i
$359$	8.48695	+	9.79447i	0.447924	+	0.516932i	0.934140	−	0.356907i	$-0.116169\pi$
$359$	8.48695	+	9.79447i	0.447924	+	0.516932i	−0.486216	+	0.873839i	$0.661623\pi$
$360$	0.626339	+	1.37149i	0.0330110	+	0.0722840i
$361$	−15.6318	+	10.0460i	−0.822729	+	0.528736i
$362$	12.9649	+	3.80684i	0.681421	+	0.200083i
$363$	−6.49655	+	7.49742i	−0.340981	+	0.393513i
$364$	−0.511882	+	0.150302i	−0.0268299	+	0.00787797i
$365$	2.70291	−	5.91856i	0.141477	−	0.309791i
$366$	−0.517081	−	3.59638i	−0.0270283	−	0.187986i
$367$	30.5314			1.59372			0.796862	−	0.604162i	$-0.206492\pi$
$367$	30.5314			1.59372			0.796862	+	0.604162i	$0.206492\pi$
$368$	1.99486	+	4.36125i	0.103989	+	0.227346i
$369$	1.05820			0.0550878
$370$	−0.343035	−	2.38586i	−0.0178335	−	0.124035i
$371$	−1.35612	+	2.96949i	−0.0704063	+	0.154168i
$372$	−0.685993	+	0.201426i	−0.0355671	+	0.0104434i
$373$	16.0353	−	18.5057i	0.830276	−	0.958190i	−0.169349	−	0.985556i	$-0.554167\pi$
$373$	16.0353	−	18.5057i	0.830276	−	0.958190i	0.999625	+	0.0273663i	$0.00871206\pi$
$374$	7.14994	+	2.09941i	0.369715	+	0.108558i
$375$	−9.80052	+	6.29841i	−0.506096	+	0.325248i
$376$	3.96442	+	8.68086i	0.204449	+	0.447681i
$377$	2.51826	+	2.90623i	0.129697	+	0.149679i
$378$	0.841254	+	0.540641i	0.0432694	+	0.0278076i
$379$	−2.56369	+	17.8309i	−0.131688	+	0.915909i	0.811666	+	0.584122i	$0.198561\pi$
$379$	−2.56369	+	17.8309i	−0.131688	+	0.915909i	−0.943354	+	0.331788i	$0.892348\pi$
$380$	0.138793	−	0.965325i	0.00711992	−	0.0495201i
$381$	4.32011	+	2.77637i	0.221326	+	0.142238i
$382$	11.6014	+	13.3888i	0.593581	+	0.685029i
$383$	−15.7539	−	34.4962i	−0.804986	−	1.76267i	−0.627608	−	0.778530i	$-0.715966\pi$
$383$	−15.7539	−	34.4962i	−0.804986	−	1.76267i	−0.177378	−	0.984143i	$-0.556761\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	−6.61691	−	1.94290i	−0.337229	−	0.0990194i
$386$	−5.12103	+	5.90998i	−0.260653	+	0.300810i
$387$	−3.70817	+	1.08882i	−0.188497	+	0.0553477i
$388$	−3.99731	+	8.75289i	−0.202933	+	0.444361i
$389$	1.16053	+	8.07165i	0.0588411	+	0.409249i	0.997860	+	0.0653838i	$0.0208272\pi$
$389$	1.16053	+	8.07165i	0.0588411	+	0.409249i	−0.939019	+	0.343865i	$0.888264\pi$
$390$	0.804369			0.0407308
$391$	−3.24155	+	7.10922i	−0.163932	+	0.359529i
$392$	1.00000			0.0505076
$393$	−0.0150730	−	0.104835i	−0.000760331	−	0.00528822i
$394$	4.89904	−	10.7274i	0.246810	−	0.540439i
$395$	5.25273	−	1.54234i	0.264294	−	0.0776036i
$396$	−2.99526	+	3.45672i	−0.150518	+	0.173707i
$397$	−14.3751	−	4.22090i	−0.721463	−	0.211841i	−0.0996682	−	0.995021i	$-0.531778\pi$
$397$	−14.3751	−	4.22090i	−0.721463	−	0.211841i	−0.621795	+	0.783180i	$0.713596\pi$
$398$	2.48936	−	1.59981i	0.124780	−	0.0801914i
$399$	−0.268702	−	0.588376i	−0.0134519	−	0.0294556i
$400$	1.78562	+	2.06071i	0.0892808	+	0.103035i
$401$	−16.7450	−	10.7613i	−0.836203	−	0.537395i	0.0510401	−	0.998697i	$-0.483746\pi$
$401$	−16.7450	−	10.7613i	−0.836203	−	0.537395i	−0.887244	+	0.461301i	$0.847383\pi$
$402$	−0.277422	+	1.92951i	−0.0138366	+	0.0962354i
$403$	−0.0542820	+	0.377540i	−0.00270398	+	0.0188066i
$404$	−4.23970	−	2.72469i	−0.210933	−	0.135558i
$405$	−0.987362	−	1.13948i	−0.0490624	−	0.0566210i
$406$	−2.99438	−	6.55677i	−0.148608	−	0.325407i
$407$	6.15140	−	3.95326i	0.304913	−	0.195956i
$408$	1.56321	+	0.458999i	0.0773902	+	0.0227238i
$409$	22.4127	−	25.8656i	1.10824	−	1.27897i	0.151358	−	0.988479i	$-0.451635\pi$
$409$	22.4127	−	25.8656i	1.10824	−	1.27897i	0.956877	−	0.290493i	$-0.0938192\pi$
$410$	−1.53087	+	0.449504i	−0.0756042	+	0.0221994i
$411$	−4.11357	+	9.00746i	−0.202907	+	0.444305i
$412$	0.412608	+	2.86975i	0.0203277	+	0.141382i
$413$	11.3841			0.560174
$414$	−3.14276	−	3.62257i	−0.154458	−	0.178040i
$415$	6.66777			0.327308
$416$	−0.0759239	−	0.528062i	−0.00372247	−	0.0258904i
$417$	6.51755	−	14.2714i	0.319166	−	0.698876i
$418$	2.83869	−	0.833513i	0.138845	−	0.0407685i
$419$	20.9596	−	24.1887i	1.02395	−	1.18170i	0.0407441	−	0.999170i	$-0.487027\pi$
$419$	20.9596	−	24.1887i	1.02395	−	1.18170i	0.983201	−	0.182526i	$-0.0584274\pi$
$420$	−1.44667	−	0.424780i	−0.0705902	−	0.0207272i
$421$	−4.09261	+	2.63016i	−0.199462	+	0.128186i	−0.636559	−	0.771228i	$-0.719643\pi$
$421$	−4.09261	+	2.63016i	−0.199462	+	0.128186i	0.437097	+	0.899414i	$0.356006\pi$
$422$	1.64247	+	3.59651i	0.0799541	+	0.175075i
$423$	−6.24951	−	7.21232i	−0.303862	−	0.350675i
$424$	−2.74627	−	1.76492i	−0.133371	−	0.0857121i
$425$	−0.632213	+	4.39714i	−0.0306668	+	0.213293i
$426$	−0.0910965	+	0.633590i	−0.00441364	+	0.0306976i
$427$	3.05658	+	1.96434i	0.147918	+	0.0950613i
$428$	−6.32473	−	7.29913i	−0.305717	−	0.352817i
$429$	1.01367	+	2.21963i	0.0489404	+	0.107165i
$430$	4.90199	−	3.15032i	0.236395	−	0.151922i
$431$	−0.206741	−	0.0607045i	−0.00995835	−	0.00292403i	0.276750	−	0.960942i	$-0.410743\pi$
$431$	−0.206741	−	0.0607045i	−0.00995835	−	0.00292403i	−0.286708	+	0.958018i	$0.592561\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	14.1181	−	4.14545i	0.678473	−	0.199218i	0.0757001	−	0.997131i	$-0.475881\pi$
$433$	14.1181	−	4.14545i	0.678473	−	0.199218i	0.602773	+	0.797913i	$0.294063\pi$
$434$	0.297002	−	0.650345i	0.0142566	−	0.0312175i
$435$	1.54668	+	10.7574i	0.0741579	+	0.515779i
$436$	16.1898			0.775353
$437$	0.443304	+	3.07024i	0.0212061	+	0.146870i
$438$	4.31541			0.206198
$439$	0.333745	+	2.32125i	0.0159288	+	0.110787i	0.996235	−	0.0866982i	$-0.0276316\pi$
$439$	0.333745	+	2.32125i	0.0159288	+	0.110787i	−0.980306	+	0.197485i	$0.936722\pi$
$440$	2.86481	−	6.27306i	0.136574	−	0.299056i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	0.569182	−	0.656871i	0.0270732	−	0.0312442i
$443$	38.0138	+	11.1619i	1.80609	+	0.530316i	0.998253	−	0.0590876i	$-0.0188191\pi$
$443$	38.0138	+	11.1619i	1.80609	+	0.530316i	0.807839	+	0.589404i	$0.200637\pi$
$444$	1.34489	−	0.864310i	0.0638258	−	0.0410183i
$445$	−5.99785	−	13.1335i	−0.284325	−	0.622585i
$446$	−14.8890	−	17.1828i	−0.705015	−	0.813630i
$447$	11.2038	+	7.20028i	0.529924	+	0.340561i
$448$	−0.142315	+	0.989821i	−0.00672374	+	0.0467647i
$449$	3.46994	−	24.1340i	0.163757	−	1.13895i	−0.727716	−	0.685878i	$-0.759418\pi$
$449$	3.46994	−	24.1340i	0.163757	−	1.13895i	0.891473	−	0.453074i	$-0.149673\pi$
$450$	−2.29385	−	1.47417i	−0.108133	−	0.0694931i
$451$	−3.16960	−	3.65791i	−0.149250	−	0.172244i
$452$	5.46583	+	11.9685i	0.257091	+	0.562951i
$453$	11.4138	−	7.33522i	0.536268	−	0.344638i
$454$	23.1057	+	6.78445i	1.08440	+	0.318410i
$455$	−0.526750	+	0.607902i	−0.0246944	+	0.0284989i
$456$	0.620628	−	0.182233i	0.0290636	−	0.00853383i
$457$	−6.39482	+	14.0027i	−0.299137	+	0.655019i	−0.998196	−	0.0600455i	$-0.980875\pi$
$457$	−6.39482	+	14.0027i	−0.299137	+	0.655019i	0.699059	+	0.715064i	$0.253603\pi$
$458$	−0.317425	−	2.20774i	−0.0148323	−	0.103161i
$459$	−1.62920			−0.0760445
$460$	6.08534	+	3.90568i	0.283730	+	0.182103i
$461$	35.9148			1.67272			0.836361	−	0.548180i	$-0.184679\pi$
$461$	35.9148			1.67272			0.836361	+	0.548180i	$0.184679\pi$
$462$	−0.650933	−	4.52734i	−0.0302841	−	0.210631i
$463$	−6.62693	+	14.5110i	−0.307980	+	0.674381i	−0.998817	−	0.0486291i	$-0.984515\pi$
$463$	−6.62693	+	14.5110i	−0.307980	+	0.674381i	0.690837	+	0.723010i	$0.257242\pi$
$464$	6.91617	−	2.03077i	0.321075	−	0.0942762i
$465$	−0.705918	+	0.814673i	−0.0327362	+	0.0377795i
$466$	−14.6017	−	4.28744i	−0.676409	−	0.198612i
$467$	13.7413	−	8.83101i	0.635873	−	0.408651i	−0.182607	−	0.983186i	$-0.558454\pi$
$467$	13.7413	−	8.83101i	0.635873	−	0.408651i	0.818480	+	0.574535i	$0.194817\pi$
$468$	0.221621	+	0.485282i	0.0102444	+	0.0224321i
$469$	−1.27656	−	1.47322i	−0.0589459	−	0.0680272i
$470$	12.1046	+	7.77917i	0.558345	+	0.358826i
$471$	0.164665	−	1.14527i	0.00758737	−	0.0527713i
$472$	−1.62012	+	11.2682i	−0.0745722	+	0.518661i
$473$	14.8707	+	9.55681i	0.683755	+	0.439422i
$474$	2.37774	+	2.74406i	0.109213	+	0.126039i
$475$	0.732673	+	1.60433i	0.0336174	+	0.0736117i
$476$	−1.37057	+	0.880812i	−0.0628200	+	0.0403719i
$477$	3.13226	+	0.919715i	0.143416	+	0.0421108i
$478$	−16.1399	+	18.6265i	−0.738224	+	0.851956i
$479$	3.96092	−	1.16303i	0.180979	−	0.0531402i	−0.189987	−	0.981787i	$-0.560845\pi$
$479$	3.96092	−	1.16303i	0.180979	−	0.0531402i	0.370966	+	0.928646i	$0.379027\pi$
$480$	0.626339	−	1.37149i	0.0285883	−	0.0625997i
$481$	−0.121378	−	0.844200i	−0.00553435	−	0.0384922i
$482$	−3.41319			−0.155467
$483$	4.79583	−	0.00286106i	0.218218	−	0.000130183i
$484$	9.92051			0.450932
$485$	2.06473	+	14.3605i	0.0937546	+	0.652078i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−13.2703	+	3.89650i	−0.601333	+	0.176567i	−0.568210	−	0.822884i	$-0.692364\pi$
$487$	−13.2703	+	3.89650i	−0.601333	+	0.176567i	−0.0331236	+	0.999451i	$0.510546\pi$
$488$	−2.37935	+	2.74591i	−0.107708	+	0.124302i
$489$	0.205561	+	0.0603582i	0.00929579	+	0.00272949i
$490$	1.26839	−	0.815148i	0.0573002	−	0.0368246i
$491$	−16.0103	−	35.0577i	−0.722536	−	1.58213i	−0.810316	−	0.585993i	$-0.800705\pi$
$491$	−16.0103	−	35.0577i	−0.722536	−	1.58213i	0.0877805	−	0.996140i	$-0.472023\pi$
$492$	−0.692975	−	0.799736i	−0.0312417	−	0.0360549i
$493$	9.87928	+	6.34903i	0.444940	+	0.285946i
$494$	0.0491097	−	0.341566i	0.00220955	−	0.0153678i
$495$	−0.981440	+	6.82607i	−0.0441124	+	0.306809i
$496$	0.601457	+	0.386533i	0.0270062	+	0.0173558i
$497$	−0.419180	−	0.483760i	−0.0188028	−	0.0216996i
$498$	1.83711	+	4.02271i	0.0823229	+	0.180262i
$499$	8.76983	−	5.63603i	0.392592	−	0.252303i	−0.329421	−	0.944183i	$-0.606854\pi$
$499$	8.76983	−	5.63603i	0.392592	−	0.252303i	0.722013	+	0.691880i	$0.243217\pi$
$500$	11.1780	+	3.28215i	0.499895	+	0.146782i
$501$	4.27100	−	4.92900i	0.190814	−	0.220211i
$502$	−25.3273	+	7.43678i	−1.13041	+	0.331920i
$503$	−2.39162	+	5.23693i	−0.106637	+	0.233503i	−0.955427	−	0.295228i	$-0.904605\pi$
$503$	−2.39162	+	5.23693i	−0.106637	+	0.233503i	0.848790	+	0.528731i	$0.177332\pi$
$504$	−0.142315	−	0.989821i	−0.00633921	−	0.0440902i
$505$	−7.59863			−0.338135
$506$	−3.10881	+	21.7142i	−0.138204	+	0.965314i
$507$	−12.7154			−0.564710
$508$	−0.730833	−	5.08306i	−0.0324255	−	0.225524i
$509$	12.4557	−	27.2742i	0.552089	−	1.20891i	−0.403710	−	0.914887i	$-0.632280\pi$
$509$	12.4557	−	27.2742i	0.552089	−	1.20891i	0.955799	−	0.294020i	$-0.0949931\pi$
$510$	2.35691	−	0.692052i	0.104366	−	0.0306446i
$511$	−2.82600	+	3.26137i	−0.125015	+	0.144275i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−0.544147	+	0.349702i	−0.0240247	+	0.0154397i
$514$	4.68005	+	10.2479i	0.206428	+	0.452015i
$515$	2.86262	+	3.30364i	0.126142	+	0.145576i
$516$	3.25121	+	2.08942i	0.143126	+	0.0919818i
$517$	−6.21203	+	43.2056i	−0.273205	+	1.90018i
$518$	−0.227515	+	1.58240i	−0.00999645	+	0.0695269i
$519$	2.63447	+	1.69307i	0.115640	+	0.0743175i
$520$	−0.526750	−	0.607902i	−0.0230995	−	0.0266583i
$521$	−10.8985	−	23.8645i	−0.477473	−	1.04552i	−0.983150	−	0.182798i	$-0.941485\pi$
$521$	−10.8985	−	23.8645i	−0.477473	−	1.04552i	0.505677	−	0.862723i	$-0.331243\pi$
$522$	−6.06389	+	3.89702i	−0.265409	+	0.170568i
$523$	24.5779	+	7.21672i	1.07472	+	0.315565i	0.770763	−	0.637122i	$-0.219875\pi$
$523$	24.5779	+	7.21672i	1.07472	+	0.315565i	0.303953	+	0.952687i	$0.401693\pi$
$524$	−0.0693582	+	0.0800436i	−0.00302993	+	0.00349672i
$525$	2.61626	−	0.768203i	0.114183	−	0.0335271i
$526$	−0.837619	+	1.83413i	−0.0365219	+	0.0799718i
$527$	0.165769	+	1.15295i	0.00722100	+	0.0502231i
$528$	4.57389			0.199053
$529$	−22.0761	−	6.45351i	−0.959828	−	0.280588i
$530$	−4.92202			−0.213799
$531$	−1.62012	−	11.2682i	−0.0703074	−	0.488999i
$532$	−0.268702	+	0.588376i	−0.0116497	+	0.0255093i
$533$	−0.541675	+	0.159050i	−0.0234625	+	0.00688922i
$534$	6.27097	−	7.23708i	0.271371	−	0.313179i
$535$	−13.9721	−	4.10258i	−0.604067	−	0.177370i
$536$	1.63990	−	1.05390i	0.0708330	−	0.0455216i
$537$	9.52379	+	20.8542i	0.410982	+	0.899924i
$538$	2.30889	+	2.66460i	0.0995434	+	0.114879i
$539$	3.84780	+	2.47283i	0.165737	+	0.106513i
$540$	−0.214574	+	1.49240i	−0.00923381	+	0.0642225i
$541$	0.391575	−	2.72346i	0.0168351	−	0.117091i	−0.979671	−	0.200611i	$-0.935707\pi$
$541$	0.391575	−	2.72346i	0.0168351	−	0.117091i	0.996506	+	0.0835203i	$0.0266163\pi$
$542$	3.59641	+	2.31127i	0.154479	+	0.0992775i
$543$	8.84864	+	10.2119i	0.379732	+	0.438234i
$544$	−0.676794	−	1.48197i	−0.0290173	−	0.0635390i
$545$	20.5351	−	13.1971i	0.879628	−	0.565302i
$546$	−0.511882	−	0.150302i	−0.0219065	−	0.00643234i
$547$	16.9281	−	19.5361i	0.723794	−	0.835303i	−0.267964	−	0.963429i	$-0.586351\pi$
$547$	16.9281	−	19.5361i	0.723794	−	0.835303i	0.991758	+	0.128126i	$0.0408963\pi$
$548$	9.50120	−	2.78980i	0.405871	−	0.119175i
$549$	1.50935	−	3.30502i	0.0644176	−	0.141055i
$550$	1.77491	+	12.3447i	0.0756822	+	0.526381i
$551$	4.66244			0.198627
$552$	−0.679686	+	4.74742i	−0.0289294	+	0.202064i
$553$	−3.63091			−0.154402
$554$	0.246144	+	1.71197i	0.0104576	+	0.0727345i
$555$	1.00131	−	2.19257i	0.0425034	−	0.0930695i
$556$	−15.0537	+	4.42017i	−0.638420	+	0.187457i
$557$	9.22291	−	10.6438i	0.390787	−	0.450993i	−0.525931	−	0.850527i	$-0.676283\pi$
$557$	9.22291	−	10.6438i	0.390787	−	0.450993i	0.916718	+	0.399535i	$0.130828\pi$
$558$	−0.685993	−	0.201426i	−0.0290404	−	0.00852703i
$559$	1.73449	−	1.11469i	0.0733613	−	0.0471464i
$560$	0.626339	+	1.37149i	0.0264677	+	0.0579561i
$561$	4.87988	+	5.63169i	0.206029	+	0.237770i
$562$	−21.5125	−	13.8252i	−0.907449	−	0.583182i
$563$	2.17922	−	15.1568i	0.0918431	−	0.638783i	−0.890954	−	0.454094i	$-0.849963\pi$
$563$	2.17922	−	15.1568i	0.0918431	−	0.638783i	0.982797	−	0.184689i	$-0.0591278\pi$
$564$	−1.35815	+	9.44613i	−0.0571884	+	0.397754i
$565$	16.6889	+	10.7253i	0.702108	+	0.451217i
$566$	−11.1235	−	12.8372i	−0.467554	−	0.539586i
$567$	0.415415	+	0.909632i	0.0174458	+	0.0382010i
$568$	0.538491	−	0.346067i	0.0225946	−	0.0145207i
$569$	5.58691	+	1.64046i	0.234215	+	0.0687718i	0.396734	−	0.917934i	$-0.370144\pi$
$569$	5.58691	+	1.64046i	0.234215	+	0.0687718i	−0.162519	+	0.986705i	$0.551962\pi$
$570$	0.638654	−	0.737046i	0.0267503	−	0.0308715i
$571$	19.7836	−	5.80900i	0.827920	−	0.243099i	0.159797	−	0.987150i	$-0.448916\pi$
$571$	19.7836	−	5.80900i	0.827920	−	0.243099i	0.668123	+	0.744051i	$0.267098\pi$
$572$	1.01367	−	2.21963i	0.0423837	−	0.0928073i
$573$	2.52123	+	17.5356i	0.105326	+	0.732559i
$574$	1.05820			0.0441685
$575$	−13.0768	+	0.00780128i	−0.545342	+	0.000325336i
$576$	1.00000			0.0416667
$577$	−4.27132	−	29.7077i	−0.177817	−	1.23675i	−0.861800	−	0.507248i	$-0.830663\pi$
$577$	−4.27132	−	29.7077i	−0.177817	−	1.23675i	0.683983	−	0.729498i	$-0.260246\pi$
$578$	−5.95942	+	13.0493i	−0.247879	+	0.542780i
$579$	−7.50326	+	2.20316i	−0.311825	+	0.0915600i
$580$	7.11706	−	8.21352i	0.295520	−	0.341048i
$581$	−4.24321	−	1.24592i	−0.176038	−	0.0516895i
$582$	−8.09492	+	5.20229i	−0.335545	+	0.215642i
$583$	−6.20275	−	13.5821i	−0.256892	−	0.562514i
$584$	−2.82600	−	3.26137i	−0.116941	−	0.134957i
$585$	0.676679	+	0.434875i	0.0279772	+	0.0179799i
$586$	−0.694791	+	4.83237i	−0.0287015	+	0.199624i
$587$	−2.52195	+	17.5406i	−0.104092	+	0.723976i	0.869209	+	0.494445i	$0.164629\pi$
$587$	−2.52195	+	17.5406i	−0.104092	+	0.723976i	−0.973301	+	0.229532i	$0.926281\pi$
$588$	0.841254	+	0.540641i	0.0346927	+	0.0222957i
$589$	0.302842	+	0.349498i	0.0124784	+	0.0144008i
$590$	7.13030	+	15.6132i	0.293550	+	0.642784i
$591$	9.92101	−	6.37585i	0.408096	−	0.262267i
$592$	−1.53392	−	0.450399i	−0.0630437	−	0.0185113i
$593$	25.4269	−	29.3443i	1.04416	−	1.20502i	0.0658599	−	0.997829i	$-0.479021\pi$
$593$	25.4269	−	29.3443i	1.04416	−	1.20502i	0.978300	−	0.207195i	$-0.0664336\pi$
$594$	−4.38862	+	1.28861i	−0.180067	+	0.0528725i
$595$	−1.02043	+	2.23443i	−0.0418336	+	0.0916029i
$596$	−1.89535	−	13.1825i	−0.0776368	−	0.539975i
$597$	2.95911			0.121108
$598$	2.15320	+	1.38197i	0.0880511	+	0.0565128i
$599$	14.1225			0.577031			0.288516	−	0.957475i	$-0.406838\pi$
$599$	14.1225			0.577031			0.288516	+	0.957475i	$0.406838\pi$
$600$	0.388051	+	2.69896i	0.0158421	+	0.110184i
$601$	−10.7315	+	23.4986i	−0.437745	+	0.958529i	0.554261	+	0.832343i	$0.313001\pi$
$601$	−10.7315	+	23.4986i	−0.437745	+	0.958529i	−0.992007	+	0.126186i	$0.959726\pi$
$602$	−3.70817	+	1.08882i	−0.151134	+	0.0443769i
$603$	−1.27656	+	1.47322i	−0.0519854	+	0.0599943i
$604$	−13.0180	−	3.82244i	−0.529697	−	0.155533i
$605$	12.5831	−	8.08668i	0.511577	−	0.328770i
$606$	−2.09358	−	4.58430i	−0.0850459	−	0.186225i
$607$	14.5423	+	16.7827i	0.590255	+	0.681190i	0.969777	−	0.243992i	$-0.0784572\pi$
$607$	14.5423	+	16.7827i	0.590255	+	0.681190i	−0.379522	+	0.925183i	$0.623912\pi$
$608$	−0.544147	−	0.349702i	−0.0220681	−	0.0141823i
$609$	1.02583	−	7.13479i	0.0415686	−	0.289116i
$610$	−0.779626	+	5.42242i	−0.0315661	+	0.219547i
$611$	4.28304	+	2.75254i	0.173273	+	0.111356i
$612$	1.06690	+	1.23127i	0.0431268	+	0.0497710i
$613$	−20.0162	−	43.8293i	−0.808445	−	1.77025i	−0.613950	−	0.789345i	$-0.710420\pi$
$613$	−20.0162	−	43.8293i	−0.808445	−	1.77025i	−0.194495	−	0.980903i	$-0.562307\pi$
$614$	1.51527	−	0.973803i	0.0611512	−	0.0392995i
$615$	−1.53087	−	0.449504i	−0.0617306	−	0.0181257i
$616$	−2.99526	+	3.45672i	−0.120683	+	0.139275i
$617$	2.86417	−	0.840997i	0.115307	−	0.0338573i	−0.223570	−	0.974688i	$-0.571771\pi$
$617$	2.86417	−	0.840997i	0.115307	−	0.0338573i	0.338877	+	0.940831i	$0.389953\pi$
$618$	−1.20440	+	2.63726i	−0.0484479	+	0.106086i
$619$	−6.74767	−	46.9311i	−0.271212	−	1.88632i	−0.435934	−	0.899979i	$-0.643582\pi$
$619$	−6.74767	−	46.9311i	−0.271212	−	1.88632i	0.164722	−	0.986340i	$-0.447327\pi$
$620$	1.07797			0.0432922
$621$	−0.685350	−	4.74661i	−0.0275021	−	0.190475i
$622$	14.8960			0.597274
$623$	1.36281	+	9.47856i	0.0545999	+	0.379751i
$624$	0.221621	−	0.485282i	0.00887193	−	0.0194268i
$625$	3.77225	−	1.10763i	0.150890	−	0.0443053i
$626$	−3.86487	+	4.46030i	−0.154471	+	0.178270i
$627$	2.83869	+	0.833513i	0.113366	+	0.0332873i
$628$	−0.973371	+	0.625548i	−0.0388417	+	0.0249621i
$629$	−1.08197	−	2.36919i	−0.0431412	−	0.0944660i
$630$	−0.987362	−	1.13948i	−0.0393374	−	0.0453978i
$631$	−11.1732	−	7.18059i	−0.444798	−	0.285855i	0.299007	−	0.954251i	$-0.403345\pi$
$631$	−11.1732	−	7.18059i	−0.444798	−	0.285855i	−0.743805	+	0.668396i	$0.766981\pi$
$632$	0.516733	−	3.59396i	0.0205545	−	0.142960i
$633$	−0.562685	+	3.91356i	−0.0223647	+	0.155550i
$634$	−0.885696	−	0.569203i	−0.0351755	−	0.0226059i
$635$	−5.07043	−	5.85159i	−0.201214	−	0.232213i
$636$	−1.35612	−	2.96949i	−0.0537737	−	0.117748i
$637$	0.448802	−	0.288428i	0.0177822	−	0.0114279i
$638$	31.6339	+	9.28854i	1.25240	+	0.367737i
$639$	−0.419180	+	0.483760i	−0.0165825	+	0.0191372i
$640$	−1.44667	+	0.424780i	−0.0571846	+	0.0167909i
$641$	−12.2370	+	26.7954i	−0.483334	+	1.05835i	0.498200	+	0.867062i	$0.333995\pi$
$641$	−12.2370	+	26.7954i	−0.483334	+	1.05835i	−0.981533	+	0.191291i	$0.938733\pi$
$642$	−1.37450	−	9.55983i	−0.0542470	−	0.377296i
$643$	30.2693			1.19371			0.596853	−	0.802351i	$-0.296418\pi$
$643$	30.2693			1.19371			0.596853	+	0.802351i	$0.296418\pi$
$644$	−3.14276	−	3.62257i	−0.123842	−	0.142749i
$645$	5.82700			0.229438
$646$	−0.149973	−	1.04309i	−0.00590062	−	0.0410397i
$647$	0.756472	−	1.65644i	0.0297400	−	0.0651215i	−0.894179	−	0.447710i	$-0.852240\pi$
$647$	0.756472	−	1.65644i	0.0297400	−	0.0651215i	0.923919	+	0.382588i	$0.124967\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−34.0983	+	39.3516i	−1.33848	+	1.54468i
$650$	1.39575	+	0.409830i	0.0547460	+	0.0160749i
$651$	0.601457	−	0.386533i	0.0235730	−	0.0151494i
$652$	−0.0889982	−	0.194879i	−0.00348544	−	0.00763205i
$653$	−1.73031	−	1.99688i	−0.0677121	−	0.0781440i	0.720883	−	0.693057i	$-0.243737\pi$
$653$	−1.73031	−	1.99688i	−0.0677121	−	0.0781440i	−0.788595	+	0.614913i	$0.789191\pi$
$654$	13.6198	+	8.75289i	0.532575	+	0.342265i
$655$	−0.0227262	+	0.158064i	−0.000887985	+	0.00617607i
$656$	−0.150598	+	1.04743i	−0.00587986	+	0.0408953i
$657$	3.63036	+	2.33309i	0.141634	+	0.0910225i
$658$	−6.24951	−	7.21232i	−0.243631	−	0.281166i
$659$	−11.3800	−	24.9187i	−0.443301	−	0.970693i	−0.990981	−	0.134005i	$-0.957216\pi$
$659$	−11.3800	−	24.9187i	−0.443301	−	0.970693i	0.547680	−	0.836688i	$-0.315511\pi$
$660$	5.80150	−	3.72840i	0.225823	−	0.145128i
$661$	25.0330	+	7.35036i	0.973671	+	0.285896i	0.729610	−	0.683864i	$-0.239702\pi$
$661$	25.0330	+	7.35036i	0.973671	+	0.285896i	0.244062	+	0.969760i	$0.421520\pi$
$662$	1.88145	−	2.17131i	0.0731248	−	0.0843905i
$663$	0.833958	−	0.244872i	0.0323882	−	0.00951005i
$664$	1.83711	−	4.02271i	0.0712937	−	0.156111i
$665$	0.138793	+	0.965325i	0.00538215	+	0.0374337i
$666$	1.59868			0.0619475
$667$	−14.3418	+	31.4537i	−0.555315	+	1.21789i
$668$	−6.52200			−0.252344
$669$	−3.23569	−	22.5047i	−0.125099	−	0.870082i
$670$	1.22096	−	2.67352i	0.0471697	−	0.103287i
$671$	−15.9454	+	4.68201i	−0.615567	+	0.180747i
$672$	−0.654861	+	0.755750i	−0.0252618	+	0.0291537i
$673$	−41.3551	−	12.1430i	−1.59412	−	0.468076i	−0.640219	−	0.768192i	$-0.721156\pi$
$673$	−41.3551	−	12.1430i	−1.59412	−	0.468076i	−0.953903	+	0.300116i	$0.902975\pi$
$674$	−16.4109	+	10.5466i	−0.632123	+	0.406241i
$675$	−1.13272	−	2.48030i	−0.0435983	−	0.0954669i
$676$	8.32681	+	9.60965i	0.320262	+	0.369602i
$677$	−19.2189	−	12.3513i	−0.738643	−	0.474697i	0.116433	−	0.993198i	$-0.462854\pi$
$677$	−19.2189	−	12.3513i	−0.738643	−	0.474697i	−0.855077	+	0.518501i	$0.826490\pi$
$678$	−1.87251	+	13.0236i	−0.0719133	+	0.500168i
$679$	1.36942	−	9.52451i	0.0525534	−	0.365517i
$680$	−2.06647	−	1.32804i	−0.0792454	−	0.0509279i
$681$	15.7698	+	18.1993i	0.604300	+	0.697400i
$682$	1.35846	+	2.97461i	0.0520180	+	0.113904i
$683$	11.1939	−	7.19390i	0.428324	−	0.275267i	−0.308666	−	0.951170i	$-0.599883\pi$
$683$	11.1939	−	7.19390i	0.428324	−	0.275267i	0.736990	+	0.675903i	$0.236246\pi$
$684$	0.620628	+	0.182233i	0.0237303	+	0.00696784i
$685$	9.77717	−	11.2835i	0.373566	−	0.431119i
$686$	−0.959493	+	0.281733i	−0.0366336	+	0.0107566i
$687$	0.926559	−	2.02888i	0.0353504	−	0.0774067i
$688$	−0.550007	−	3.82538i	−0.0209688	−	0.145841i
$689$	−1.74158			−0.0663490
$690$	3.00774	+	6.57565i	0.114503	+	0.250331i
$691$	12.2500			0.466012			0.233006	−	0.972475i	$-0.425144\pi$
$691$	12.2500			0.466012			0.233006	+	0.972475i	$0.425144\pi$
$692$	−0.445673	−	3.09972i	−0.0169419	−	0.117834i
$693$	1.90006	−	4.16056i	0.0721775	−	0.158047i
$694$	12.0265	−	3.53129i	0.456518	−	0.134046i
$695$	−15.4910	+	17.8775i	−0.587606	+	0.678134i
$696$	6.91617	+	2.03077i	0.262157	+	0.0769762i
$697$	−1.45034	+	0.932077i	−0.0549356	+	0.0353050i
$698$	−10.7179	−	23.4689i	−0.405679	−	0.888313i
$699$	−9.96574	−	11.5011i	−0.376939	−	0.435011i
$700$	−2.29385	−	1.47417i	−0.0866995	−	0.0557184i
$701$	−4.02000	+	27.9597i	−0.151833	+	1.05602i	0.761311	+	0.648387i	$0.224556\pi$
$701$	−4.02000	+	27.9597i	−0.151833	+	1.05602i	−0.913144	+	0.407637i	$0.866353\pi$
$702$	−0.0759239	+	0.528062i	−0.00286556	+	0.0199304i
$703$	−0.869915	−	0.559060i	−0.0328095	−	0.0210854i
$704$	−2.99526	−	3.45672i	−0.112888	−	0.130280i
$705$	5.97732	+	13.0885i	0.225119	+	0.492942i
$706$	−22.2307	+	14.2868i	−0.836663	+	0.537691i
$707$	4.83559	+	1.41986i	0.181861	+	0.0533992i
$708$	−7.45499	+	8.60352i	−0.280176	+	0.323340i
$709$	−37.5471	+	11.0248i	−1.41011	+	0.414046i	−0.896144	−	0.443764i	$-0.853643\pi$
$709$	−37.5471	+	11.0248i	−1.41011	+	0.414046i	−0.513967	+	0.857810i	$0.671825\pi$
$710$	0.400923	−	0.877900i	0.0150464	−	0.0329470i
$711$	0.516733	+	3.59396i	0.0193790	+	0.134784i
$712$	−9.57603			−0.358877
$713$	−3.28933	+	0.967966i	−0.123186	+	0.0362506i
$714$	−1.62920			−0.0609713
$715$	−0.523591	−	3.64165i	−0.0195812	−	0.136190i
$716$	9.52379	−	20.8542i	0.355921	−	0.779357i
$717$	−23.6480	+	6.94369i	−0.883152	+	0.259317i
$718$	8.48695	−	9.79447i	0.316730	−	0.365526i
$719$	28.3478	+	8.32366i	1.05719	+	0.310420i	0.763720	−	0.645547i	$-0.223371\pi$
$719$	28.3478	+	8.32366i	1.05719	+	0.310420i	0.293473	+	0.955967i	$0.405189\pi$
$720$	1.26839	−	0.815148i	0.0472703	−	0.0303788i
$721$	−1.20440	−	2.63726i	−0.0448540	−	0.0982167i
$722$	12.1684	+	14.0430i	0.452860	+	0.522628i
$723$	−2.87136	−	1.84531i	−0.106787	−	0.0686279i
$724$	1.92299	−	13.3747i	0.0714675	−	0.497067i
$725$	−2.79713	+	19.4545i	−0.103883	+	0.722522i
$726$	8.34566	+	5.36343i	0.309737	+	0.199056i
$727$	25.6037	+	29.5482i	0.949588	+	1.09588i	0.995291	+	0.0969281i	$0.0309017\pi$
$727$	25.6037	+	29.5482i	0.949588	+	1.09588i	−0.0457032	+	0.998955i	$0.514553\pi$
$728$	0.221621	+	0.485282i	0.00821381	+	0.0179857i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−6.24298	−	1.83310i	−0.231063	−	0.0678462i
$731$	4.12326	−	4.75850i	0.152504	−	0.175999i
$732$	−3.48619	+	1.02364i	−0.128853	+	0.0378347i
$733$	−7.02276	+	15.3777i	−0.259392	+	0.567989i	−0.993859	−	0.110656i	$-0.964705\pi$
$733$	−7.02276	+	15.3777i	−0.259392	+	0.567989i	0.734467	+	0.678644i	$0.237432\pi$
$734$	−4.34506	−	30.2206i	−0.160379	−	1.11546i
$735$	1.50774			0.0556140
$736$	4.03296	−	2.59523i	0.148657	−	0.0956614i
$737$	8.91615			0.328430
$738$	−0.150598	−	1.04743i	−0.00554359	−	0.0385565i
$739$	12.4851	−	27.3385i	0.459271	−	1.00566i	−0.528382	−	0.849007i	$-0.677201\pi$
$739$	12.4851	−	27.3385i	0.459271	−	1.00566i	0.987653	−	0.156657i	$-0.0500718\pi$
$740$	−2.31276	+	0.679086i	−0.0850186	+	0.0249637i
$741$	0.225978	−	0.260793i	0.00830151	−	0.00958046i
$742$	3.13226	+	0.919715i	0.114989	+	0.0337638i
$743$	−32.8114	+	21.0866i	−1.20373	+	0.773592i	−0.979598	−	0.200966i	$-0.935592\pi$
$743$	−32.8114	+	21.0866i	−1.20373	+	0.773592i	−0.224135	+	0.974558i	$0.571956\pi$
$744$	0.297002	+	0.650345i	0.0108886	+	0.0238428i
$745$	−13.1497	−	15.1756i	−0.481769	−	0.555991i
$746$	−20.5994	−	13.2384i	−0.754198	−	0.484694i
$747$	−0.629366	+	4.37734i	−0.0230273	+	0.160158i
$748$	1.06050	−	7.37594i	0.0387757	−	0.269691i
$749$	8.12494	+	5.22158i	0.296879	+	0.190792i
$750$	7.62906	+	8.80440i	0.278574	+	0.321491i
$751$	17.1379	+	37.5269i	0.625372	+	1.36937i	0.911547	+	0.411197i	$0.134889\pi$
$751$	17.1379	+	37.5269i	0.625372	+	1.36937i	−0.286174	+	0.958178i	$0.592384\pi$
$752$	8.02831	−	5.15948i	0.292762	−	0.188147i
$753$	−25.3273	−	7.43678i	−0.922979	−	0.271011i
$754$	2.51826	−	2.90623i	0.0917097	−	0.105839i
$755$	−19.6279	+	5.76326i	−0.714332	+	0.209747i
$756$	0.415415	−	0.909632i	0.0151085	−	0.0330830i
$757$	3.57120	+	24.8382i	0.129797	+	0.902760i	0.945809	+	0.324725i	$0.105272\pi$
$757$	3.57120	+	24.8382i	0.129797	+	0.902760i	−0.816011	+	0.578036i	$0.803819\pi$
$758$	18.0142			0.654306
$759$	−14.3549	+	16.5864i	−0.521049	+	0.602048i
$760$	−0.975252			−0.0353761
$761$	−3.84447	−	26.7389i	−0.139362	−	0.969283i	−0.932739	−	0.360553i	$-0.882588\pi$
$761$	−3.84447	−	26.7389i	−0.139362	−	0.969283i	0.793377	−	0.608731i	$-0.208321\pi$
$762$	2.13329	−	4.67126i	0.0772810	−	0.169222i
$763$	−15.5340	+	4.56121i	−0.562370	+	0.165127i
$764$	11.6014	−	13.3888i	0.419725	−	0.484389i
$765$	2.35691	+	0.692052i	0.0852144	+	0.0250212i
$766$	−31.9030	+	20.5028i	−1.15270	+	0.740798i
$767$	2.52295	+	5.52449i	0.0910984	+	0.199478i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	−17.5254	−	11.2629i	−0.631983	−	0.406151i	0.185061	−	0.982727i	$-0.440752\pi$
$769$	−17.5254	−	11.2629i	−0.631983	−	0.406151i	−0.817043	+	0.576577i	$0.804388\pi$
$770$	−0.981440	+	6.82607i	−0.0353686	+	0.245994i
$771$	−1.60332	+	11.1513i	−0.0577420	+	0.401604i
$772$	6.57863	+	4.22783i	0.236770	+	0.152163i
$773$	15.7036	+	18.1229i	0.564818	+	0.651835i	0.964271	−	0.264919i	$-0.0853452\pi$
$773$	15.7036	+	18.1229i	0.564818	+	0.651835i	−0.399453	+	0.916754i	$0.630800\pi$
$774$	1.60546	+	3.51547i	0.0577071	+	0.126361i
$775$	−1.64000	+	1.05396i	−0.0589105	+	0.0378595i
$776$	9.23268	+	2.71096i	0.331434	+	0.0973178i
$777$	−1.04691	+	1.20820i	−0.0375577	+	0.0433439i
$778$	7.82433	−	2.29743i	0.280516	−	0.0823669i
$779$	−0.284342	+	0.622621i	−0.0101876	+	0.0223077i
$780$	−0.114474	−	0.796182i	−0.00409882	−	0.0285079i
$781$	2.92778			0.104764
$782$	7.49818	+	2.19681i	0.268134	+	0.0785577i
$783$	−7.20816			−0.257598
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	−0.724705	+	1.58688i	−0.0258658	+	0.0566383i
$786$	−0.101623	+	0.0298391i	−0.00362476	+	0.00106433i
$787$	−15.5343	+	17.9276i	−0.553738	+	0.639048i	−0.961750	−	0.273928i	$-0.911677\pi$
$787$	−15.5343	+	17.9276i	−0.553738	+	0.639048i	0.408012	+	0.912977i	$0.366222\pi$
$788$	−11.3154	−	3.32251i	−0.403095	−	0.118359i
$789$	−1.69625	+	1.09012i	−0.0603883	+	0.0388092i
$790$	−2.27418	−	4.97977i	−0.0809118	−	0.177172i
$791$	−8.61634	−	9.94378i	−0.306362	−	0.353560i
$792$	3.84780	+	2.47283i	0.136726	+	0.0878683i
$793$	−0.275859	+	1.91864i	−0.00979604	+	0.0681329i
$794$	−2.13215	+	14.8294i	−0.0756672	+	0.526277i
$795$	−4.14067	−	2.66105i	−0.146854	−	0.0943776i
$796$	−1.93780	−	2.23634i	−0.0686836	−	0.0792651i
$797$	14.0548	+	30.7756i	0.497845	+	1.09013i	0.977164	+	0.212488i	$0.0681565\pi$
$797$	14.0548	+	30.7756i	0.497845	+	1.09013i	−0.479319	+	0.877641i	$0.659116\pi$
$798$	−0.544147	+	0.349702i	−0.0192626	+	0.0123793i
$799$	14.9181	+	4.38035i	0.527764	+	0.154966i
$800$	1.78562	−	2.06071i	0.0631310	−	0.0728571i
$801$	9.18814	−	2.69788i	0.324647	−	0.0953249i
$802$	−8.26874	+	18.1060i	−0.291979	+	0.639346i
$803$	−2.80905	−	19.5373i	−0.0991291	−	0.689458i
$804$	1.94936			0.0687485
$805$	−6.93920	−	2.03304i	−0.244575	−	0.0716551i
$806$	0.381422			0.0134350
$807$	0.501770	+	3.48989i	0.0176632	+	0.122850i
$808$	−2.09358	+	4.58430i	−0.0736520	+	0.161275i
$809$	−50.5614	+	14.8462i	−1.77764	+	0.521963i	−0.994944	−	0.100436i	$-0.967976\pi$
$809$	−50.5614	+	14.8462i	−1.77764	+	0.521963i	−0.782700	+	0.622399i	$0.786158\pi$
$810$	−0.987362	+	1.13948i	−0.0346924	+	0.0400371i
$811$	−8.36683	−	2.45672i	−0.293799	−	0.0862672i	0.131511	−	0.991315i	$-0.458017\pi$
$811$	−8.36683	−	2.45672i	−0.293799	−	0.0862672i	−0.425311	+	0.905047i	$0.639835\pi$
$812$	−6.06389	+	3.89702i	−0.212801	+	0.136759i
$813$	1.77592	+	3.88873i	0.0622843	+	0.136384i
$814$	−4.78846	−	5.52618i	−0.167835	−	0.193692i
$815$	−0.271740	−	0.174637i	−0.00951863	−	0.00611725i
$816$	0.231859	−	1.61262i	0.00811670	−	0.0564529i
$817$	0.355760	−	2.47437i	0.0124465	−	0.0865671i
$818$	−28.7920	−	18.5035i	−1.00669	−	0.646959i
$819$	−0.349363	−	0.403186i	−0.0122077	−	0.0140885i
$820$	0.662794	+	1.45132i	0.0231458	+	0.0506822i
$821$	−12.7349	+	8.18423i	−0.444451	+	0.285632i	−0.743662	−	0.668555i	$-0.766913\pi$
$821$	−12.7349	+	8.18423i	−0.444451	+	0.285632i	0.299211	+	0.954187i	$0.403277\pi$
$822$	9.50120	+	2.78980i	0.331392	+	0.0973056i
$823$	15.9507	−	18.4081i	0.556007	−	0.641666i	−0.406265	−	0.913755i	$-0.633169\pi$
$823$	15.9507	−	18.4081i	0.556007	−	0.641666i	0.962272	+	0.272089i	$0.0877146\pi$
$824$	2.78182	−	0.816816i	0.0969093	−	0.0284551i
$825$	−5.18092	+	11.3446i	−0.180377	+	0.394970i
$826$	−1.62012	−	11.2682i	−0.0563713	−	0.392071i
$827$	31.1767			1.08412			0.542060	−	0.840340i	$-0.317645\pi$
$827$	31.1767			1.08412			0.542060	+	0.840340i	$0.317645\pi$
$828$	−3.13844	+	3.62632i	−0.109068	+	0.126023i
$829$	−27.7746			−0.964653			−0.482327	−	0.875991i	$-0.660208\pi$
$829$	−27.7746			−0.964653			−0.482327	+	0.875991i	$0.660208\pi$
$830$	−0.948923	−	6.59990i	−0.0329376	−	0.229086i
$831$	−0.718490	+	1.57327i	−0.0249241	+	0.0545762i
$832$	−0.511882	+	0.150302i	−0.0177463	+	0.00521079i
$833$	1.06690	−	1.23127i	0.0369659	−	0.0426609i
$834$	−15.0537	−	4.42017i	−0.521268	−	0.153058i
$835$	−8.27247	+	5.31639i	−0.286280	+	0.183981i
$836$	−1.22902	−	2.69117i	−0.0425064	−	0.0930761i
$837$	−0.468195	−	0.540326i	−0.0161832	−	0.0186764i
$838$	−26.9254	−	17.3039i	−0.930121	−	0.597753i
$839$	−2.52023	+	17.5286i	−0.0870082	+	0.605155i	0.898936	+	0.438080i	$0.144341\pi$
$839$	−2.52023	+	17.5286i	−0.0870082	+	0.605155i	−0.985944	+	0.167075i	$0.946568\pi$
$840$	−0.214574	+	1.49240i	−0.00740352	+	0.0514926i
$841$	19.3131	+	12.4118i	0.665968	+	0.427992i
$842$	3.18583	+	3.67664i	0.109791	+	0.126705i
$843$	−10.6230	−	23.2610i	−0.365874	−	0.801153i
$844$	3.32615	−	2.13759i	0.114491	−	0.0735788i
$845$	18.3950	+	5.40125i	0.632806	+	0.185809i
$846$	−6.24951	+	7.21232i	−0.214863	+	0.247965i
$847$	−9.51866	+	2.79493i	−0.327065	+	0.0960350i
$848$	−1.35612	+	2.96949i	−0.0465694	+	0.101973i
$849$	−2.41736	−	16.8131i	−0.0829635	−	0.577024i
$850$	4.44235			0.152372
$851$	6.44740	−	4.14893i	0.221014	−	0.142224i
$852$	0.640106			0.0219297
$853$	5.73182	+	39.8657i	0.196254	+	1.36497i	0.815035	+	0.579411i	$0.196718\pi$
$853$	5.73182	+	39.8657i	0.196254	+	1.36497i	−0.618782	+	0.785563i	$0.712373\pi$
$854$	1.50935	−	3.30502i	0.0516490	−	0.113096i
$855$	0.935747	−	0.274760i	0.0320019	−	0.00939660i
$856$	−6.32473	+	7.29913i	−0.216175	+	0.249479i
$857$	−5.01842	−	1.47354i	−0.171426	−	0.0503352i	0.194893	−	0.980824i	$-0.437564\pi$
$857$	−5.01842	−	1.47354i	−0.171426	−	0.0503352i	−0.366319	+	0.930489i	$0.619382\pi$
$858$	2.05277	−	1.31924i	0.0700805	−	0.0450380i
$859$	7.60034	+	16.6424i	0.259320	+	0.567832i	0.993849	−	0.110745i	$-0.0353238\pi$
$859$	7.60034	+	16.6424i	0.259320	+	0.567832i	−0.734528	+	0.678578i	$0.762597\pi$
$860$	−3.81588	−	4.40375i	−0.130120	−	0.150167i
$861$	0.890217	+	0.572108i	0.0303385	+	0.0194974i
$862$	−0.0306644	+	0.213275i	−0.00104443	+	0.00726419i
$863$	−3.08341	+	21.4456i	−0.104961	+	0.730017i	0.867582	+	0.497293i	$0.165673\pi$
$863$	−3.08341	+	21.4456i	−0.104961	+	0.730017i	−0.972543	+	0.232723i	$0.925236\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−3.09202	−	3.56838i	−0.105132	−	0.121329i
$866$	−6.11247	−	13.3844i	−0.207710	−	0.454822i
$867$	−12.0684	+	7.75588i	−0.409864	+	0.263403i
$868$	−0.685993	−	0.201426i	−0.0232841	−	0.00683683i
$869$	10.8755	−	12.5510i	0.368928	−	0.425765i
$870$	10.4278	−	3.06188i	0.353536	−	0.103808i
$871$	0.432017	−	0.945986i	0.0146384	−	0.0320535i
$872$	−2.30406	−	16.0251i	−0.0780252	−	0.542677i
$873$	−9.62246			−0.325671
$874$	2.97590	−	0.875733i	0.100661	−	0.0296221i
$875$	−11.6499			−0.393838
$876$	−0.614148	−	4.27149i	−0.0207501	−	0.144320i
$877$	4.39037	−	9.61358i	0.148252	−	0.324627i	−0.820907	−	0.571062i	$-0.806532\pi$
$877$	4.39037	−	9.61358i	0.148252	−	0.324627i	0.969159	+	0.246434i	$0.0792590\pi$
$878$	2.25013	−	0.660697i	0.0759381	−	0.0222974i
$879$	−3.19707	+	3.68962i	−0.107835	+	0.124448i
$880$	−6.61691	−	1.94290i	−0.223056	−	0.0654952i
$881$	−25.3320	+	16.2799i	−0.853457	+	0.548484i	−0.892651	−	0.450748i	$-0.851157\pi$
$881$	−25.3320	+	16.2799i	−0.853457	+	0.548484i	0.0391939	+	0.999232i	$0.487521\pi$
$882$	0.415415	+	0.909632i	0.0139878	+	0.0306289i
$883$	14.8000	+	17.0801i	0.498060	+	0.574792i	0.948001	−	0.318266i	$-0.103101\pi$
$883$	14.8000	+	17.0801i	0.498060	+	0.574792i	−0.449941	+	0.893058i	$0.648555\pi$
$884$	−0.731188	−	0.469906i	−0.0245925	−	0.0158047i
$885$	−2.44273	+	16.9896i	−0.0821115	+	0.571098i
$886$	5.63832	−	39.2154i	0.189423	−	1.31747i
$887$	−2.55026	−	1.63895i	−0.0856294	−	0.0550307i	0.497125	−	0.867679i	$-0.334389\pi$
$887$	−2.55026	−	1.63895i	−0.0856294	−	0.0550307i	−0.582755	+	0.812648i	$0.698025\pi$
$888$	−1.04691	−	1.20820i	−0.0351320	−	0.0405445i
$889$	2.13329	+	4.67126i	0.0715483	+	0.156669i
$890$	−12.1462	+	7.80588i	−0.407141	+	0.261654i
$891$	−4.38862	−	1.28861i	−0.147024	−	0.0431702i
$892$	−14.8890	+	17.1828i	−0.498521	+	0.575323i
$893$	5.92282	−	1.73910i	0.198199	−	0.0581966i
$894$	5.53251	−	12.1145i	0.185035	−	0.405170i
$895$	−4.91932	−	34.2146i	−0.164435	−	1.14367i
$896$	1.00000			0.0334077
$897$	1.06424	+	2.32669i	0.0355341	+	0.0776861i
$898$	−24.3822			−0.813643
$899$	0.733419	+	5.10104i	0.0244609	+	0.170129i
$900$	−1.13272	+	2.48030i	−0.0377572	+	0.0826767i
$901$	−5.10308	+	1.49840i	−0.170008	+	0.0499189i
$902$	−3.16960	+	3.65791i	−0.105536	+	0.121795i
$903$	−3.70817	−	1.08882i	−0.123400	−	0.0362336i
$904$	11.0688	−	7.11349i	0.368143	−	0.236591i
$905$	−8.46325	−	18.5319i	−0.281328	−	0.616023i
$906$	−8.88491	−	10.2537i	−0.295181	−	0.340657i
$907$	13.7381	+	8.82894i	0.456166	+	0.293160i	0.748474	−	0.663164i	$-0.230787\pi$
$907$	13.7381	+	8.82894i	0.456166	+	0.293160i	−0.292308	+	0.956324i	$0.594423\pi$
$908$	3.42711	−	23.8361i	0.113733	−	0.791027i
$909$	0.717229	−	4.98844i	0.0237890	−	0.165456i
$910$	0.676679	+	0.434875i	0.0224317	+	0.0144160i
$911$	−15.8684	−	18.3131i	−0.525744	−	0.606741i	0.429315	−	0.903155i	$-0.358755\pi$
$911$	−15.8684	−	18.3131i	−0.525744	−	0.606741i	−0.955060	+	0.296413i	$0.904209\pi$
$912$	−0.268702	−	0.588376i	−0.00889762	−	0.0194831i
$913$	17.0163	−	10.9357i	0.563159	−	0.361920i
$914$	14.7703	+	4.33694i	0.488557	+	0.143453i
$915$	−3.58744	+	4.14013i	−0.118597	+	0.136869i
$916$	−2.14009	+	0.628388i	−0.0707107	+	0.0207625i
$917$	0.0439978	−	0.0963417i	0.00145293	−	0.00318148i
$918$	0.231859	+	1.61262i	0.00765250	+	0.0532243i
$919$	−17.0596			−0.562745			−0.281373	−	0.959599i	$-0.590790\pi$
$919$	−17.0596			−0.562745			−0.281373	+	0.959599i	$0.590790\pi$
$920$	2.99989	−	6.57923i	0.0989035	−	0.216911i
$921$	1.80120			0.0593516
$922$	−5.11122	−	35.5493i	−0.168329	−	1.17075i
$923$	0.141861	−	0.310632i	0.00466940	−	0.0102246i
$924$	−4.38862	+	1.28861i	−0.144375	+	0.0423923i
$925$	2.85462	−	3.29441i	0.0938594	−	0.108319i
$926$	15.3064	+	4.49435i	0.502998	+	0.147694i
$927$	−2.43901	+	1.56746i	−0.0801077	+	0.0514821i
$928$	−2.99438	−	6.55677i	−0.0982952	−	0.215236i
$929$	−37.4975	−	43.2744i	−1.23025	−	1.41979i	−0.874373	−	0.485254i	$-0.838727\pi$
$929$	−37.4975	−	43.2744i	−1.23025	−	1.41979i	−0.355879	−	0.934532i	$-0.615818\pi$
$930$	0.906843	+	0.582793i	0.0297366	+	0.0191105i
$931$	0.0920533	−	0.640245i	0.00301693	−	0.0209832i
$932$	−2.16576	+	15.0632i	−0.0709419	+	0.493412i
$933$	12.5313	+	8.05337i	0.410256	+	0.263655i
$934$	−10.6967	−	12.3447i	−0.350007	−	0.403930i
$935$	−4.66735	−	10.2201i	−0.152639	−	0.334232i
$936$	0.448802	−	0.288428i	0.0146696	−	0.00942755i
$937$	−6.18988	−	1.81751i	−0.202215	−	0.0593756i	0.179057	−	0.983839i	$-0.442695\pi$
$937$	−6.18988	−	1.81751i	−0.202215	−	0.0593756i	−0.381271	+	0.924463i	$0.624514\pi$
$938$	−1.27656	+	1.47322i	−0.0416810	+	0.0481025i
$939$	−5.66276	+	1.66274i	−0.184797	+	0.0542614i
$940$	5.97732	−	13.0885i	0.194959	−	0.426900i
$941$	0.441806	+	3.07283i	0.0144025	+	0.100171i	0.995755	−	0.0920469i	$-0.0293410\pi$
$941$	0.441806	+	3.07283i	0.0144025	+	0.100171i	−0.981352	+	0.192218i	$0.938432\pi$
$942$	−1.15705			−0.0376987
$943$	−3.32568	−	3.83342i	−0.108299	−	0.124833i
$944$	11.3841			0.370520
$945$	−0.214574	−	1.49240i	−0.00698010	−	0.0485477i
$946$	7.34321	−	16.0794i	0.238748	−	0.522786i
$947$	20.0727	−	5.89386i	0.652274	−	0.191525i	0.0611788	−	0.998127i	$-0.480514\pi$
$947$	20.0727	−	5.89386i	0.652274	−	0.191525i	0.591095	+	0.806602i	$0.298696\pi$
$948$	2.37774	−	2.74406i	0.0772255	−	0.0891230i
$949$	−2.20898	−	0.648616i	−0.0717066	−	0.0210550i
$950$	1.48373	−	0.953536i	0.0481386	−	0.0309368i
$951$	−0.437361	−	0.957687i	−0.0141824	−	0.0310551i
$952$	1.06690	+	1.23127i	0.0345784	+	0.0399056i
$953$	10.4331	+	6.70493i	0.337960	+	0.217194i	0.698602	−	0.715511i	$-0.253806\pi$
$953$	10.4331	+	6.70493i	0.337960	+	0.217194i	−0.360642	+	0.932704i	$0.617442\pi$
$954$	0.464586	−	3.23127i	0.0150415	−	0.104616i
$955$	3.80137	−	26.4391i	0.123010	−	0.855550i
$956$	20.7339	+	13.3248i	0.670581	+	0.430956i
$957$	21.5903	+	24.9166i	0.697916	+	0.805438i
$958$	−1.71489	−	3.75509i	−0.0554056	−	0.121321i
$959$	−8.33036	+	5.35360i	−0.269001	+	0.172877i
$960$	−1.44667	−	0.424780i	−0.0466910	−	0.0137097i
$961$	19.9659	−	23.0419i	0.644063	−	0.743288i
$962$	−0.818334	+	0.240284i	−0.0263841	+	0.00774708i
$963$	4.01213	−	8.78535i	0.129289	−	0.283104i
$964$	0.485748	+	3.37845i	0.0156449	+	0.108813i
$965$	11.7906			0.379553
$966$	−0.685350	−	4.74661i	−0.0220508	−	0.152720i
$967$	27.7918			0.893725			0.446863	−	0.894603i	$-0.352541\pi$
$967$	27.7918			0.893725			0.446863	+	0.894603i	$0.352541\pi$
$968$	−1.41184	−	9.81953i	−0.0453781	−	0.315612i
$969$	0.437770	−	0.958582i	0.0140632	−	0.0307941i
$970$	13.9205	−	4.08743i	0.446961	−	0.131239i
$971$	−31.8336	+	36.7380i	−1.02159	+	1.17898i	−0.0378679	+	0.999283i	$0.512057\pi$
$971$	−31.8336	+	36.7380i	−1.02159	+	1.17898i	−0.983722	+	0.179695i	$0.942489\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	13.1986	−	8.48225i	0.423129	−	0.271928i
$974$	5.74540	+	12.5807i	0.184094	+	0.403110i
$975$	0.952612	+	1.09937i	0.0305080	+	0.0352081i
$976$	3.05658	+	1.96434i	0.0978387	+	0.0628771i
$977$	−0.696835	+	4.84660i	−0.0222937	+	0.155056i	−0.997927	−	0.0643495i	$-0.979503\pi$
$977$	−0.696835	+	4.84660i	−0.0222937	+	0.155056i	0.975634	+	0.219406i	$0.0704119\pi$
$978$	0.0304894	−	0.212059i	0.000974944	−	0.00678089i
$979$	−36.8467	−	23.6799i	−1.17763	−	0.756814i
$980$	−0.987362	−	1.13948i	−0.0315401	−	0.0363992i
$981$	6.72551	+	14.7268i	0.214729	+	0.470191i
$982$	−32.4224	+	20.8366i	−1.03464	+	0.664922i
$983$	−48.0573	−	14.1109i	−1.53279	−	0.450067i	−0.596886	−	0.802326i	$-0.703596\pi$
$983$	−48.0573	−	14.1109i	−1.53279	−	0.450067i	−0.935903	+	0.352258i	$0.885414\pi$
$984$	−0.692975	+	0.799736i	−0.0220912	+	0.0254947i
$985$	−17.0608	+	5.00949i	−0.543601	+	0.159616i
$986$	4.87844	−	10.6823i	0.155361	−	0.340193i
$987$	−1.35815	−	9.44613i	−0.0432303	−	0.300674i
$988$	−0.345078			−0.0109784
$989$	15.5982	+	10.0112i	0.495994	+	0.318338i
$990$	6.89626			0.219178
$991$	−0.113611	−	0.790179i	−0.00360896	−	0.0251009i	0.987937	−	0.154854i	$-0.0494907\pi$
$991$	−0.113611	−	0.790179i	−0.00360896	−	0.0251009i	−0.991546	+	0.129753i	$0.958582\pi$
$992$	0.297002	−	0.650345i	0.00942984	−	0.0206485i
$993$	2.75668	−	0.809435i	0.0874806	−	0.0256866i
$994$	−0.419180	+	0.483760i	−0.0132956	+	0.0153439i
$995$	−4.28085	−	1.25697i	−0.135712	−	0.0398486i
$996$	3.72032	−	2.39090i	0.117883	−	0.0757587i
$997$	15.5777	+	34.1103i	0.493350	+	1.08028i	0.978574	+	0.205895i	$0.0660106\pi$
$997$	15.5777	+	34.1103i	0.493350	+	1.08028i	−0.485225	+	0.874390i	$0.661262\pi$
$998$	−6.82674	−	7.87848i	−0.216097	−	0.249389i
$999$	1.34489	+	0.864310i	0.0425505	+	0.0273456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.463.2	yes	40
23.8	even	11	inner	966.2.q.i.169.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.169.2	✓	40	23.8	even	11	inner
966.2.q.i.463.2	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.987362 + 1.13948i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.987362 + 1.13948i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(1.26839 + 0.815148i) q^{10} +(-0.650933 + 4.52734i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(0.448802 + 0.288428i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(0.626339 + 1.37149i) q^{15} +(0.841254 - 0.540641i) q^{16} +(1.56321 + 0.458999i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.620628 - 0.182233i) q^{19} +(0.626339 - 1.37149i) q^{20} +(-0.142315 - 0.989821i) q^{21} +4.57389 q^{22} +(-0.679686 + 4.74742i) q^{23} +1.00000 q^{24} +(0.388051 + 2.69896i) q^{25} +(0.221621 - 0.485282i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(6.91617 + 2.03077i) q^{29} +(1.26839 - 0.815148i) q^{30} +(0.297002 + 0.650345i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(3.84780 + 2.47283i) q^{33} +(0.231859 - 1.61262i) q^{34} +(-0.214574 + 1.49240i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-1.04691 - 1.20820i) q^{37} +(-0.268702 - 0.588376i) q^{38} +(0.448802 - 0.288428i) q^{39} +(-1.44667 - 0.424780i) q^{40} +(-0.692975 + 0.799736i) q^{41} +(-0.959493 + 0.281733i) q^{42} +(1.60546 - 3.51547i) q^{43} +(-0.650933 - 4.52734i) q^{44} +1.50774 q^{45} +(4.79583 - 0.00286106i) q^{46} +9.54327 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(2.61626 - 0.768203i) q^{50} +(1.06690 - 1.23127i) q^{51} +(-0.511882 - 0.150302i) q^{52} +(-2.74627 + 1.76492i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-4.51609 - 5.21185i) q^{55} +(0.841254 + 0.540641i) q^{56} +(0.0920533 - 0.640245i) q^{57} +(1.02583 - 7.13479i) q^{58} +(9.57690 + 6.15470i) q^{59} +(-0.987362 - 1.13948i) q^{60} +(1.50935 + 3.30502i) q^{61} +(0.601457 - 0.386533i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.771787 + 0.226617i) q^{65} +(1.90006 - 4.16056i) q^{66} +(-0.277422 - 1.92951i) q^{67} -1.62920 q^{68} +(4.03606 + 2.59041i) q^{69} +1.50774 q^{70} +(-0.0910965 - 0.633590i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-4.14061 + 1.21579i) q^{73} +(-1.04691 + 1.20820i) q^{74} +(2.61626 + 0.768203i) q^{75} +(-0.544147 + 0.349702i) q^{76} +(1.90006 + 4.16056i) q^{77} +(-0.349363 - 0.403186i) q^{78} +(-3.05452 - 1.96302i) q^{79} +(-0.214574 + 1.49240i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.890217 + 0.572108i) q^{82} +(-2.89602 - 3.34219i) q^{83} +(0.415415 + 0.909632i) q^{84} +(-2.06647 + 1.32804i) q^{85} +(-3.70817 - 1.08882i) q^{86} +(4.72034 - 5.44756i) q^{87} +(-4.38862 + 1.28861i) q^{88} +(-3.97803 + 8.71067i) q^{89} +(-0.214574 - 1.49240i) q^{90} +0.533492 q^{91} +(-0.685350 - 4.74661i) q^{92} +0.714954 q^{93} +(-1.35815 - 9.44613i) q^{94} +(-0.405134 + 0.887120i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(6.30137 - 7.27217i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(3.84780 - 2.47283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

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